>>Jest jakaś różnica między many a time a many times? Czy też oba wyrazenia oznaczaja ,,czesto"?
Tak , many a member has been put in jail = many members have been put ..
'many' here is a predeterminer followed by the indefinite article ( as a central one again) and a singualr count noun, it's literary, formal. Grammatical concord is singular because the noun is singular but notionally it's plural, hence the ‘clash’.
inverted : "Many a time have I ridden straight into the house, mounted on my cuddy"
There's this heart-rending example, I like it :
"The woods decay, the woods decay and fall, The vapours weep their burthen to the
ground, Man comes and tills the field and lies beneath, And after many a summer
dies the Swan".