Question 1] a) The letter came to me only yesterday. --> Only yesterday did the letter come to me. In intro adverbial inversion, when [Only yesterday] is emphasized, the aux.
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b) Only yesterday come the letter to me.
Is b) grammatically correct? No. "came" is what you want - and no inversion. "Only yesterday the letter came to me"
Dcomest's question:
Do native speakers commonly use the construction [not... in the least]?
CalifJim's answer:
I don't use it often. I would add "bit" and use something like "The rich are not the least bit happy"
(But I would not use either one without "bit"!)