"Will you be free tomorrow?"
Translation:Fyddi di yn rhydd yfory?
"Chi'n", "chi yn", "di'n", "di yn" - sometimes "yn" is accepted, sometimes not.
It would be byddwch not fyddwch because there is nothing to mutate it. Unless it was 'a fyddwch chi'n'
No, the mutation is required at the start of questions, though you are correct that this was due to the "a" interogative particle but even though we drop it today it's considered correct to mutate the verb.