I have never heard any (australian) english speaker say "will you be in work tomorrow" we would say "will you be at work tomorrow?" "Are you in work?" Would mean "Have you got a job?"
As a Canadian English speaker I agree with you. I may also hear 'will you be in at work tomorrow. '
No, because both of those suggestions need the verb 'to work' rather than the noun 'work'.
'Yn y gwaith' is literally 'In the work' which refers to a place of work, this is usually transposed to English as 'In work'.
The second suggestion is similar to the one above:- 'Will you be working tomorrow = Fyddwch chi'n gweithio yfory'
The first suggestion would be 'Weithiwch chi yfory'