Inversion with intro adverbial

Looking into inversion, I found a website listing different types of inversion, but I can't understand intro adverbial.

The website says that inversions in this case are optional, and gives the following examples:

Into the room ran the lady.

First comes love, then comes marriage.

After A comes B, then comes C, next comes D.

Down came the rain and washed the spider out.

Now, these examples are extremely hard for me to "restructure", I hope I can receive some help, this is the best I was able to come with:

Into the room, the lady ran.

First comes love, marriage comes then.

After A comes B, C comes then, D comes next.

Your first de-inversion is quite correct: “Into the room(,) the lady ran”. This is easier to de-invert than the others simply because the inverted form is somewhat stilted and awkward in Modern English (but still mandatory in other Germanic languages), while the non-inverted form is much more natural.

The correct de-inversion of the three latter phrases would be (with extra punctuation, just to make it extra clear):

First, love comes; then, marriage comes.
After A, B comes; then, C comes; next, D comes.
Down the rain came and washed the spider out.

In the first two of these sentences, there is a distinct semantic and syntactic difference between inverted “First comes love, then (comes) marriage” and non-inverted “First, love comes; then, marriage (comes)” (similarly for the phrases with ‘after’, ‘then’, ‘next’):

• With no inversion, ‘first/after/then/next’ functions as a sentential adverb, creating a frame for the entire sentence to function in: “What happens first/after/then/next is that …”.
• With inversion, the adverbial has a narrower scope, being a true adverb, attached only to the verb, describing not that the coming of love is the first thing to happen, but rather that love is the first thing to come.

Sentential adverbs are outside the clause itself and act as ‘comments’ to the clause they belong to; therefore, as they are not inside the clause, no inversion takes place. If an adverb is a member of the clause, though, inversion as a rule occurs. Some adverbs often function as sentential adverbs, while others do not—for example, ‘never’ is almost exclusively used within clauses, never sententially: “Never have I heard such nonsense!” is perfectly common, but “Never(,) I have heard such nonsense!” doesn’t work at all.

In the third example, ‘down’ is slightly more complex. ‘Down’ does not, for semantic reasons, normally function as a sentential adverb (it is hard to envisage a context where the framework for the sentence to occur within should be ‘down’)—and yet, it can still be used both with and without inversion. When it appears clause-initially (in the deeper structure), it causes inversion as any normal adverb (“Down came the rain”). But even when it appears post-verbally (“The rain came down”), it can be fronted to the head of the clause for focus in the same way that for examples objects can (“I know Jim, but Jake I haven’t met” where ‘Jake’ is moved to the head of the clause for focus). Such focusing does not cause inversion, and therefore the phrase ends up looking syntactically identical to one with a sentential adverb; only semantically is there a difference.

The second example, as you can see, is also ample proof that inverted forms can often be much easier and straightforward than non-inverted ones. When you have many adverbs like that, placing them all outside the scope of the clause only results in clunky, unmanageable structures.

I assume you mean this site for your examples.

There are a number of ways to structure the sentences, each with different degrees of inversion. I'm not sure which one you're looking for, but hopefully this will help.

The lady ran into the room. (subject-verb-phrase) STANDARD FORM

Into the room ran the lady. (phrase-verb-subject)

Into the room the lady ran. (phrase-subject-verb)

Another example:

Love comes first, then marriage comes. (subject-verb-modifier) then (subject-verb) STANDARD FORM

First comes love, then comes marriage. (modifier-verb-subject) then (verb-subject)

First love comes, then comes marriage. (modifier-subject-verb) then (verb-subject)