The original usage of past participles

I have heard that the origin of the present perfect construction is that sentences like "I have it done" (passive) changed to "I have done it" (present perfect).

Is that true at all?

If that's the case, would anyone mind giving me an explanation in detail on how the change took place?

Moreover, if the passive construction used to be the only usage of past participles, why are they called "past participle" in the first place?

This is far from being a complete answer to an interesting question, but in ‘An Invitation of Old English and Anglo-Saxon England’, Bruce Mitchell provides some evidence that the past participle was seen as an adjective in the ancestor of modern perfect constructions. There were three forms in Old English that correspond, for example, to our past perfect construction. One is: Hie hæfdon ϸone cyning ofslægenne, ‘They had the king, slain.’ Ofslægenne is inflected as an adjective here, showing the -ne ending of the accusative masculine singular. It agrees with ϸone cyning, the object of hæfdon. Similarly, the ancestor of today’s passive is seen in patterns like He wæs / wearϸ ofslægen ‘He was / became slain’ Hie wæron / wurdon ofslægene ‘They were / became slain’. In the second, the participle is again inflected as an adjective.

As for the term itself, I suspect we use ‘past participle’ simply because most of our traditional grammar terms are based on descriptions of Latin grammar. Latin had present active and future active participles and perfect passive and future passive participles. The perfect passive participle has come to be understood as a past participle when applied to English.

1°) It is to be noted that the English perfect and the French perfect have developed pretty much in the same way and at the same time for reasons that are known : the influence of French grammar and syntax on old English, like 'of-genitives' (instead of saxon -es/'s for example). However the French perfect has become a real past tense in French, now called "le passé composé".

You can understand the parallel between "I have it done" (passive) and "I have done it" from intuition. But there is interference with modern grammar in which "I have it done" means "somebody (else) does it for me." Yet, the original model of the syntax meant (roughly) : "I have it done (by myself)", that is is located relative to 'I'. The repetition of the subject pronoun makes it disappear in this structure because it is not a form of insistence. Therefore only the object remains to be spoken about and we obtain what must be called "a passive participle" do + -en = done. In the "active", 'do' (for ex.) means that you find the agent to the left (or before do in the spoken chain and they object to the right (or after the verb).

The passive flexion -en simply means that the order is reverted: done means that you find the object to the left (or before do) and the agent to the right (or after done) in the spoken chain. It indicates the reversal of positions.

Now the perfect is a complex structure with two verbs. In the logical order of operations, the first is the lexical verb, here do, which is affected by -en. The consequence is that the object becomes the topic and the agent can even be deleted.

The second verb is the operator have, which in its formal use is not lexical and expresses location relative to the subject of the sentence. Contrary to the active do, the passive participle done means that the process of the verb is finished (probably because the topicalised object is now fully achieved and clearly defined. This is how the perfect aspect (not tense) is still present and expressed the benefit for the subject of a completed process (typically) in the form of its completed object.

Now, the syntax of English (and French) has always easily managed auxiliaries (be in the passive; modals; now do/does/did, etc.) So what happened when the combination of this simple passive form was combined with have was not that the object took up the final position : I <have done> IT. But rather, it was that the passive participle combined with what became an overt auxiliary have in the Verb Phrase: I have <DONE IT>.

For many verbs that were not transitive (no object) or reflexive, in early Middle English, the auxiliary was be, as in French the auxiliary is être ('be') for many verbs of this type : “Je me suis lavé” = I have washed, etc. This still exists in English in very rare expressions such as: "I'm done" meaning 'I have finished' (not 'I'm nearly dead, of course!) or: 'I'm finished' = 'I have finished' in standard English.