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.
These can be analysed either as instances of Subject-dependent inversion, or as Subject-postposing. One reason for choosing the latter is that postposing of the Subject is entirely optional. Notice that in the Original Poster's examples the two instances of so are quite different. They are both used as anaphoric pro-forms, but are being used to represent quite different types of phrase or clause which both have very different grammatical functions:
So says the preacher.
So began the fight.
In the first sentence so is the Complement of the verb say and represents a content clause. In (2) so is an Adjunct meaning something like in this way. When anaphoric so is preposed like this, we can also postpose the Subject. This is optional as can be seen from the examples below:
- So the preacher says.
- So the fight began.
(Notice that so must be stressed in the last example - probably to distinguish this usage from the usage of so as a connective or conjunction.)
The grammatical status of the proform so makes a big difference to the effect of postposing the Subject. When so is the pro-clause Complement of the verb say, the Subject postposing is quite normal. However, fronting of so used as a manner adjunct gives quite a literary effect: So endeth the lesson, So began my first term and so forth.
So is not a conjunction or conventional discourse connective in either of the Original Poster's sentences - although the word so can be used as a connective as is illustrated below:
- He took my ice-cream, so I punched him on the nose.
Best Answer
Your answer is not only perfectly acceptable, but a more accurate rendering than the one they want.
In their answer they have tacitly applied an implication (which is not even a logical implication, but a material one) that 'X is difficult' => 'X occurs rarely'. I think this is inappropriate in a grammar book.