a key to open any door

[navit]

Which are correct:
1) I can make a key to open any door. The lock on this one seems strange, but I can make a special key specifically for this lock.
2) I can make a key that opens any door. The lock on this one seems strange, but I can make a special key specifically for this lock.

3) Can you make a key to open any door? The lock on this one looks strange. I doubt you can make a key to open it.
4) Can you make a key that opens any door? The lock on this one looks strange. I doubt you can make a key to open it.

Gratefully,
Navi

[Alan]

All are, of course, grammatically possible.

I presume that you intent is to check the semantic equivalence of the infinitive vs. the relative clause construction, and indeed, 'a key to open' would naturally be understood as meaning 'a key that can open'.