Can I call an assistant professor "Professor"? My former teacher, who had done her PhD in a top-10 university in the UK in 2009, is an assistant professor in my former school.
On the day when I visited my former school, I saw her at the school canteen unexpectedly. I smiled and nodded to her before I said "Good afternoon, Professor Aiko." We were talking for a few minutes before she went back to her office. When I was sitting on a subway train on my way home, however, I was wondering
if it was impolite for me to call her that.
Can I call an assistant professor a professor, and say "Hello Prof. Nickname"?
Yes, you can call any kind of professor a professor, and you should.  Addressing someone as "assistant professor" or "associate professor" would be...well, it's simply not done, so I can't say if it would be rude or just weird.

It is similar to military protocol, actually: e.g. if someone is a rear or vice admiral, you call them admiral.  In contrast to the above example, I'm sure some knowledgeable party could be specific about what bad thing could happen to you if you screw that up!