Hi Georgey,
I cannot help with MBAE not starting, but for the BSODs try following please
- Open Bitdefender and go to the modules,
- Go to the firewall settings,
- Disable 'Block port scans in the network',
- Reboot your system
The crashes are caused by a driver conflict between Bitdefender Firewall and Malwarebytes Web Protection.
There are many different solutions you could try aside from this one, but this one works for most.
Bitdefender & Malwarebytes are working on fixing this problem so you can enable the firewall settings again.