Well let me correct your text first

Generally, your Russian is very good.
1. I think "Максим видит, что..." in this context would be better.
....
In the given context (as you described), both "открывать" and "открыть" are possible. However, "открывать" better expresses the long expectation. "Открыть" does not convey this nuance, it is a simple statement of permission to do something.