Can Flynn be compelled to answer questions under oath now that he has been granted a pardon?

In theory yes, but he can always say "I don't remember" if he doesn't want to comply and since he recently called for armed rebellion against the government I doubt he would be cooperative.

A man claims he did not remember his password to an encipher drive and he spend a few years repeat a few years in prison under a charge of contempt of court as the Judge did not believe him so I do not remember is not a get out of jail free card.

And then the fact he has already admitted guilt would mean he was lying.

Hey, that's clever.

He could claim a Fifth Amendment right to not incriminate himself on state charges.

He withdrew his guilty plea.

And it would not necessarily mean that he was lying even if he had not withdrawn it. Sometimes innocent people are pressured into pleading guilty despite their innocence.