Total Commander

I moved TC to /system/app and I see strange changes in file/folder properties dialog: I cannot see owner and cannot change it (only date/time and read/write permissions).
It's bug or some feature? Maybe limitation?

You need to move the files *.so to /system/lib, otherwise TC will not find them:
libtcmadmin.so
libtcmadmin21.so
libtcunrar.so
libtcnative.so

Thanks for your answer!
I solved the problem differently (and probably more correctly), but I was curious It is interesting, I didn't think that the path to libraries will become a problem (relative path?).

Well, that's where both Android and TC look for libraries. libtcmadmin* isn't really a library, it's a program disguised as a library. TC runs it in elevated shell (su) to perform operations like copying in root mode. The other two are libraries used for unpacking RAR files, password encryption, and other native code tasks.