The inversion between a subject and verbs

I classified the inversion into two categories according to whether only the verb 'be' or an auxiliary verb is inverted or whether the a verb phrase is inverted.

1. When a verb phrase inverted:
1) When a complement fronted:
a. Easier for us to solve would be a problem calculus.
2) When a adverb (phrase) indicating a place or a direction fronted:
b. To many men has come the realization that making the right decision is often difficult.
c. Under a tree was lying one of the biggest men I had ever seen.
d. Here and there could be seen wild animal tracks.
e. To the servants were left the silver dog collars but not the dogs.
f. On the stairs had been left a pair of shoes.
3) In a structure consisting of 'first', 'next', 'now', or 'then' and 'come' and a subject:
g. First had come the Persians and then the Muslim Arabs.

2. When the verb 'be' or an auxiliary verb inverted:
1) When a negative word or phrase fronted:
h. Never have I dreamed of such a weird thing.
i. No sooner had he arrived home than the phone rang.
j. At no time would he admit that his team played badly.
k. In no way, shape of form, would I give succor to the enemy.
2) When the word 'only' fronted:
l. Only on Sunday can I see my wife.
3) When the word 'so' or 'such' fronted:
m. So little has the way of life altered here that it is easy to imagine yourself back in the 13th century.
4) When in a 'if' clause, the word 'if' omitted:
n. Had the plane not been diverted, they would have arrived early.

I don't know which category other kinds of adverbs I haven't included in this categories is included in.
See the below sentence

o. Many a time have I seen it.
p. Well do i remember her phone number.
q. Bitterly did I regret the perverse, superstitious folly that had induced me to neglect so obvious a precaution.
r. Gladly would he now have consented to the terms.
s. With difficulty can I conceive of a mental condition in which.

I'd like to know whether fronting of adverbs of manner, time adverbs, and emphatic adverbs is common
and whether when those kinds of adverbs is fronted, only the verb 'be' or an auxiliary verb is inverted.

In advance, thank you for your help.