Switching to RGB and Back to File's Color Profile?

[TechnicGeek]

Sometimes when I open files I get the following dialog:

   

Does that mean for example if I opened file with Epson RGB Profile, I have to convert to RGB to work with it and then at the end of my project convert back to Epson RGB?

Are there CMYK profiles that files have? Like if I open design for print with CMYK profile, must I convert it to RGB to work with it or I can work without conversion?

The goal is to have completed project print-ready.

Thanks