FOGRA39 is fine for sheet fed offset-printing in Europe (central Europe at least).
For web fed offset printed magazines you may want to use either ISO Coated v2 300 (ECI) or PSO LWC Improved (ECI) if you have no further information.
And for newspapers ISOnewpaper26v4.
You may want to read up (in the Help or other resources) on Color Management, though, to get a grasp on factors like Render Intent.
And better not use »Assign Profile« unless you are certain you understand what this does.
Will be printed CMYK image as well, as it looks?
That would naturally depend on your monitor and how regularly it is calibrated.
And as for previewing separations and out-of-gamut-warnings you could check out
»Identify out-of-gamut colors« in the Help
If CMYK image has little muted colors or bright, I can modify them before printing? Or the'm faking?
Is it preferable to a high-resolution monitor for proper viewing of documents?
Thanks for the help and resources.
If CMYK image has little muted colors or bright, I can modify them before printing?
You can still edit the separated CMYK-file with Adjustment Layers for example (best keep the original rgb-file and the layered cmyk-file, though), but you should take care not to exceed the TAC (Total Area Coverage).