Hello Catalin,
What you describe reflects, up to a certain point, the functionality of the "Advanced uploading of files" assignment type. If the portfilio is to be limited in size (no more than 20 files), you could use this assignment for the purpose within one course.
If you need a true portfolio, to be used throughout the studies of a student, the best solution would be to set up a Mahara environment and network it with your Moodle. Mahara is a dedicated, open source, e-portfolio which can be closely integrated with Moodle.
And to answer your last question, a professor cannot peek in the private files of a student (or else they would not be private), but a student can submit files from their private files and link to them too.
Rgrds,
Paul.