Does the GIMP Palette *.gpl format supports only 8-bit colors?
If so, how I can store, for example, 16-bit int colors? (Yes, I know at least one answer: I will store my colors in special layer in my custom template).

Yes, gpl palettes only support 8 bit colors. There has been discussion on the create mailing list for a new palette format that should be more flexible, but that never got to any conclusion, so Krita doesn't support that yet.