I will be bringing my young baby, can I bring my diaper bag and will I be allowed to bring his baby snacks and water?

They will inspect your bag but all that should be fine as long as water and baby food is unopened.

I have seen others bring baby stuff with them

I believe you can do that the water just has to be unopened and they will inspect your bag but I believe you can do that

Yes you can

No one has said they have a problem with you bringing baby snacks.