Hi
Spybot S&D is a great tool and I'd recommend to use it for scanning in future.
Those files aren't on your pc anymore.
Yes you should install and run a scan with malwarebytes. Post the log to here when ready.
The internet connection problem and BitDefender - have you allowed legit applications like Internet Exlporer, Mozilla Firefox etc to connect the internet?
Please make sure that you don't have the Windows Firewall running along with the BitDefender firewall. Running 2 firewalls can cause problems. Instructions for disabling Windows firewall (when BitDefender's firewall is on) -> Link
