Conclusions:
I. Some Barbers are not Carpenters.
II. Every Carpenters can be Trainers. Statements:

From Statement I. Only a few Carpenters are Trainers (I) + Some Trainers are Barbers (I) → No conclusion. Hence conclusion I does not follow. Only a few Carpenters are Trainers → Some Carpenters are Trainers (I). Hence conclusion II does not follow.   From Statement II. All Barbers are Trainers (A) + Only a few Trainers are Painter (I) → No conclusion. Hence conclusion I does not follow. Only a few Trainers are Painter (I) + Some Painter are Carpenters (I) → Probable conclusion → All Carpenters can be Trainers (I). Hence conclusion II follows.   From Statement III. No Carpenter is a Painter (E) + Few Painter are Barbers (I) → Some Barbers are not Carpenters (O*). Hence conclusion I follows. Only a few Trainers are Carpenters → All Carpenters can be Trainers (I). Hence conclusion II follows. From Statement IV. All Barbers are Carpenters (A) → I.I. → Some Barbers are Carpenters (I). Hence conclusion I does not follow. No Trainer is a Barber (E) + All Barbers are Carpenters (A) → Some Carpenters are not Trainers (O*) + All Trainers are Painter (A) → Probable conclusion → All Carpenters can be Trainers (I). Hence conclusion II follows.