Is there any risk of catching an STD if I finger a girl then touch my penis or my eye by mistake?

Also can I catch an STD if my condom doesn't roll all the way to the base of my penis. It goes most of the way down but there is like a centimeter or two showing.

You can still get some STDs while using a condom, it does not protect against all, and it is not 100% in protection (both as birth control and STD prevention).

I'm not a medical professional, so I would just be guessing at the first one, but I would say that there is a definite chance that you could catch an STD that way (it's a transfer of bodily fluids even though it is indirect).