Where do “‑ess” and “‑ine” suffixes come from?

Executive Summary/TL;DR: There are at least three different -ess suffixes involved here: one is for feminines of people and critters; one is to change adjectives into nouns of quality, the way English -ness does; and one that is used to create names of fabled or mythical lands.

Plus heroine for a female hero comes to us via Latin, not German, and the Latin is using the Greek ‑ine suffix. However, the homophonic word for the drug heroin did come to us via German.

Details follow.

First -ess suffix < Fr. -esse < L. -issa

The ‑ess that denotes female persons or animals derives from French ‑esse, from Common Romanic ‑essa from Late Latin ‑issa. Because it was in Common Romanic, it is no surprise that you should find it in Italian, Spanish, and Portuguese as well; for example, Spanish princesa and poetisa.

Adaptations of this form into English occurred at several stages of history, and not all prospered, as this entry from the OED shows:

• ‑ess, suffix¹, forming sbs. denoting female persons or animals, is a. Fr. ‑esse:‑Com. Romanic ‑essa:‑late L. ‑issa, a. Gr. ‑ισσα (:‑‑ikyā: cf. the OE. fem. agent‑suffix ‑icge: ‑igjôn) occurring in class. Gr. only in βασίλισσα queen (f. βασιλ‑εύς king), but after the analogy of this employed in several late formations, as βαλάνισσα bathing‑woman, πανδόκισσα female innkeeper. A few of these (notably διακόνισσα, L. diaconissa deaconess) were adopted into late L. together with their correlative masculines, and many new derivatives of the same pattern were formed in Latin, whence they descended into the Romanic langs.; e.g. from abbātem abbot, was formed abbātissa, whence Fr.abbesse abbess. On the analogy of these the suffix became in Romanic the usual means of forming feminine derivatives expressing sex. In ME. many words in ‑esse were adopted from Fr., as countess, duchess, hostess, lioness, mistress, princess, and several which were formed on sbs. in ‑ëor, ‑ier (see ‑er²), as †devoureresse, enchantress,†espyouresse, sorceress. In imitation of these the suffix was in 14th c. appended to Eng. agent‑nouns in ‑er, as in Wyclif’s dwelleresse, sleeress (f. sleer = slayer), and to other native words, as in goddess. In 15th c.derivatives in ‑er + ‑ess gradually superseded the older Eng. fem. agent‑nouns in ‑ster (OE. ‑estre), which no longer had an exclusively feminine sense; subsequently the sbs. in ‑ster (exc. spinster) came to be regarded as properly masc., and new feminines in ‑ess were formed on them, as seamstress, songstress. By writers of 16th and succeeding centuries derivatives in ‑ess were formed very freely; many of these are now obsolete or little used, the tendency of mod. usage being to treat the agent‑nouns in ‑er, and the sbs. indicating profession or occupation, as of common gender, unless there be some special reason to the contrary. Of the words of Eng. formation still in current use, examples are authoress, giantess, Jewess, patroness, poetess, priestess, quakeress, tailoress. In Eng. the suffix is not used to form feminines of names of animals: lioness, tigress being adoptions from Fr. When ‑ess is added to a sb. in ‑ter, ‑tor, the vowel before the r is usually elided, as in actress, doctress, protectress, waitress; the derivatives with ending ‑tress, f. L. agent‑nouns in ‑tor, have in most cases been suggested by, and may be regarded as virtual adaptations of, the corresponding Fr. words in ‑trice: ‑L. ‑trīcem. The substitution of governess (already in Caxton) for the earlier governeresse f. governor was perh. due to false analogy with pairs of words like adulter‑er, ‑ess, cater‑er, ‑ess, sorcer‑er, ‑ess; in conqueress, murderess, adventuress the similar phenomenon is sufficiently explained by phonetic reasons. The existence of such words, in which ‑ess has the appearance of being added directly to vbs., gave rise in the 17th. c. to formations like confectioness, entertainess, instructess; but none of these obtained general currency.

As you see, the issue is complicated. Some of these ‑ess words came via French and often Latin before that, but others were formed independently. Even English actress was probably formed separately from French actrice (cf. Spanish actriz, both from Latin actrix, -ic-), although occasionally actrice is found in English instead of actress.

I would say that this ‑ess suffix is reasonably productive in English, at least insofar as that people would understand you if you coined something like jaguaress by analogy with lioness and leopardess. I wouldn’t try cheetess < cheetah though, because people might think you meant something deriving from a cheater.

Second -ess suffix < Fr. -esse < L. -itia

The second ‑ess suffix is one for changing adjectives into nouns. It is not a noun suffix like the first one.

‑ess, suffix², ME. ‑esse, in sbs. a. Fr., represents OF. ‑esse, ‑ece, = Pr. ‑ezza, ‑eza, Sp. ‑eza, It. ‑ezza :‑L. ‑itia, appended to adjs. to form nouns of quality; examples are duress, †humblesse, largess, prowess, †richesse (now riches). These words have been imitated in the pseudo-archaic idlesse, but otherwise the suffix scarcely occurs as an Eng. formative.

Words like finesse, noblesse, politesse, tristesse are direct borrowings from French, where the suffix was not to make feminine nouns, but rather the same thing we use -ness for in English, so those correspond to fineness, nobleness (nobility), politeness, “*tristness” (sadness) using the normal English -ness suffix. The OED says of finesse in particular:

Etymology: a. Fr. finesse = Pr. and Sp. fineza, Cat. finesa, Ital.finezza :‑Com. Rom. *finitia, f. fino fine a. (Many of the early examples may belong to fineness; cf. the spellings playnes, prophaness for plainness, profaneness.)

Words like tristesse are found in other Romance languages, like tristeza (sadness) in Spanish. I wouldn’t call it productive in English based on the OED saying that it scarcely occurs as a formative. I suppose you might get away with using them productively in English, provided you wanted to convey a snooty feel to it.

Third -ess suffix < Fr. -ois

The fourth ‑esse suffix is found in proper nouns like Lyonesse and Westernesse. Both were Middle English names used in medieval chivalric romances. This one corresponds to the modern French ‑ois suffix. Of the former, Wikipedia writes:

Lyonesse is an English alteration of French Léoneis or Léonois (earlier Loönois), a development of Lodonesia, the Latin name for Lothian in Scotland. Continental writers of Arthurian romances were often puzzled by the internal geography of Great Britain; thus it is that the author French Prose Tristan appears to place Léonois contiguous, by land, to Cornwall. In English adaptations of the French tales, Léonois, now "Lyonesse", becomes a kingdom wholly distinct from Lothian, and closely associated with the Cornish region, though its exact geographical location remained unspecified.

Presumably the formerly rare Westernesse was built by analogy on the same model as Lyonesse, but using western as a base. The name appears in King Horn, and was once rare. However, J.R.R. Tolkien adopted it as a Common Tongue translation of his Atlantis calque, Númenor. In his letter to Milton Waldman, published as #131 of his Letters, Tolkien writes:

A name that Lewis derives from me and cannot be restrained from using, and mis-spelling as Numinor. Númenóre means in ‘Elvish’ simply Westernesse or Land in the West, and is not related to numen numinous, or νούμενον!

And in Letter #275 to W.H. Auden, he spells this out more explicitly:

I have often used Westernesse as a translation. This is derived from rare Middle English Westernesse (known to me only in MS. C of King Horn) where the meaning is vague, but may be taken to mean ‘Western lands’ as distinct from the East inhabited by the Paynim and Saracens. Lewis took no part in ‘research into Númenor’.

Subsequent to publication of The Lord of the Rings, the word Westernesse has appeared in print much more often than it did in the 19^th century, where it was only in reference to discussion of King Horn. And Jack Vance took up Lyonesse and made it his own.

Probably because of Tolkien and Vance, more recent authors of fantasy (and of fantasy rôle-playing games) have used the ‑esse suffix for similar constructions to create their own mythical lands, so in this regard alone might it be said to be productive.

Epic Heroes and Heroines: -ine is Greek

Your supposition that heroine uses a Germanic suffix to form a feminine from hero turns out to be wrong. Yes, German has such a suffix (e.g. Königin queen < König king) but that is not what is going on here. Rather, heroine was but ‘recently’ adopted into English directly from the Latin, and thence from the Greek where it originated, as shown by the OED’s etymology entry for the word:

Etymology: ad. L. hērōīna, ‑īnē, a. Gr. ἡρωῑ́νη, fem. of ἥρως hero: see ‑ine. Cf. Fr. héroïne (16th c.). The Lat. form was also in Eng. use in 17th c.

So ‑ine was a Greek suffix, and we got the Greek word via Latin.

Indeed, here are OED citations showing how heroina initially competed with heroine:

• A. 1659 Cleveland Mt. Ida ᴠ, ― Next Pallas that brave Heroina came.
• 1662 Evelyn Chalcogr. 61 ― A Sardonix which he cut, representing the head of that famous Heroine [Queen Elizabeth].
• 1697 tr. C’tess D’Aunoy’s Trav. (1706) 85 ― To distinguish herself from among the Heroina’s of the most famous Ages.
• 1725 Pope Odyss. xɪ. Argt., ― He sees the shades of the ancient heroines.
• 1835 Thirlwall Greece I. v. 149 ― Medea seems··to have descended··from the rank of a goddess into that of a heroine.

The OED entry on this form of -ine is:

-ine, suffix³, forming sbs., repr. F. ‑ine, L. ‑īna, Gr. ‑ῑνη, forming feminine titles, as in Gr. ἡρωίνη, L. hērōīna, F. héroine heroine. With this the Ger. landgräfin, markgräfin, Du. landgravin, markgravin (the suffix of which is orig. the same as ‑en² 1), have fallen together in French and in Eng., as landgravine, margravine.

The only relationship between ‑ine as a feminine and anything Germanic is the isolated word vixen, where the ‑en was added to make the female fox. The OED says of this form:

-en, suffix² :-WGer. ‑innja, repr. OTeut. ‑inî, occurs in several OE. fem. sbs., a few of which have survived into mod. Eng.

1. It is used to form feminines from sbs. denoting male persons or animals, as in OE. gyden goddess (f. god), mynecen nun (f. munuc monk), wylfen she-wolf (f. wulf wolf). The only surviving instance of this use is vixen female fox.
2. It is added in a few instances to the stem of a vb. or to that of a verbal-abstract sb., as in burden sb., burian, OE. rǽden condition.

I can find no direct connection between Germanic ‑en for feminines and Greek ‑ine for the sames, but perhaps it exists further back toward PIE. The PIE gender situation is unclear; its feminine gender appears to have come into play a bit later. There seem to have been only masculine/animate vs neuter/inanimate originally.

In any event, I would not use ‑ine as a productive suffix for forming feminines in English if I were you; you’ll get more traction out of using ‑ess for that.