Is it weird to contact a professor in foreign university for research internship opportunity if I am not a student?

It's not weird, but do be prepared to have your email ignored or politely declined. Professors regularly get such emails, especially if they're famous.

In particular, what you should do is to show the professor what you can do to help them in their research. Which works of theirs are you going to focus on? What does your experience mean for the professor?

Good luck!

sure you can. but be ready for "no positive" answers. its life. you can try 100 times or 1000 times, sooner or later you will get

No, not weird at all. People have all reasons to be out of the university for some time (due to work, child care, army service or whatever). Sometimes though people don't understand how the system works in general. Once in a while I receive messages asking for "opportunity to do research in my lab", but I have no idea what is their specific request, i.e., what they want me to do in practical terms.

I cannot bring outsiders to the lab, they should have some official status at our university (such as a degree student or a research student). However in this case they should contact admission section, not me.