With regard to the above, please let me know if this is a problem with f-secure or it is a malware problem.
When you have multiple fshoster32.exe running (more than 10), that's not malware. We have built a reliability mechanism in our product so that if one component crashes 2 times, it will separate all components into different processes to limit the damage of the crash. This has triggered in your computer. Quite often it is caused by Windows failing to resume from sleep properly and killing and restarting the services.
Our product keeps working normally in this situation and you're protected.
You can recover from this by simply rebooting your Windows and the number of fshoster32.exe processes should return to normal. (If you know how, you can just restart F-Secure Hoster service to have same effect)
With the information given, we have no way of knowing. Sometimes, this can be a symptom of having more than one anti-virus program installed, as this can cause conflicts.
If you suspect malware, then a scan with www.Malwarebytes.org may answer that question.
Depends which version of Malwarebytes. If it's the free one, which I don't think runs in real time, then it will be OK to stay, and you can just run a scan with it periodically. Malwarebytes 2.02 is fine to run in real time, as it is compatible with F-Secure, but Malwarebytes 3.0 may give you problems, as it did me.
I would still recommend that you run the AVG Remover tool, as the auto-uninstall F-Secure carried out may not have removed all of AVG's components, and this may lead to problems further on.