1. Can I pay in installments? <- Fine.
2. Can I pay on an installment plan? <- Fine.
3. I'd like to pay in installments at 0% interest for 12 months. <- delete 'a'.
These two are a bit odd:
4. I'd like to pay in a 12 months installment.
5. I'd like to pay in a 12 monthly installment.
4 doesn't really work. In 5, it's not clear if you are talking about one installment (which isn't really an installment at all) or one every year, or one every month. If you tell me which you mean, I can tell you how to word it. It needs to be worded correctly to avoid ambiguity.