Did you get it Alex? Cause you didn't reply or anything!
For your questions:
1. It was me (or I?) who opened the file. --» It was "I" who opened the file. [I opened the file✔- Me opened the file✘]

2. It was he (or him?) who opened the file. --» It was he who opened the file. [ He opened the file✔ - Him opened the file ✘]

3. It is me (or I?) who opened the file . --» "I"

4. It is he (or him?) who opened the file. --» "he"

¤¤ is it OK to use 'is' in 3 and 4??? --» yes it is. Both are correct (was/is)

5. It is me (or I?) who thinks about it all the time. --» "I"
¤¤Does this structure make sense at all??? --» you should say, "think" and not "thinks" .

And in the end, as I heard It's not uncommon (at least in the U.S.) to make mistakes in these kind of cases. *even by native English speakers*
But to be grammatically correct, you should follow the structure that is explained.

Good luck!