is it normal for babies to start wearing 3-6 months clothes at 2 months and 1 week ??

It can be yes

My son does

My son has always been long, so he's always been in bigger clothes. He's 12 months and wears 18 months clothes.

Yup that's normal my son is 11 months and he's wearing 18 month clothes

My son at 3 months started wearing 6-9 months

Yes