Why my theme option not working?

A little tricky to say by looking at code alone.

The first thing you need to check in such cases – if your validation function receives data from submitted form. var_dump() input and die; right after that to stop execution and prevent redirect back.

Depending on what you get there (if anything) check back through Settings API functions. There are a lot of arguments to juggle with those and it is easy to mix then up.

Hata!: SQLSTATE[HY000] [1045] Access denied for user 'divattrend_liink'@'localhost' (using password: YES)