Session Files Question

Do not worry. It will not get full. The "garbage" (old session files) will automatically be removed periodically.
How often this happens depends on the PHP.ini settings session.gc_probability and session.gc_divisor.
Read about these settings here. The default values are usually just fine.

The garbage collector is triggered when the session library is loaded.

What about if I use database instead does it delete old sessions from database in time like files garbage?

There's only one rule - please don't tell anyone to go and read the manual.  Sometimes the manual just SUCKS!