This was supposed to be an Antivirus program.
But after installing this program many of our colleagues have been
facing some issues like a performance problem, application slow
responsiveness, slow network connection.
That is completely normal and expected behavior from many Antivirus programs, especially during scheduled scans. In other words, those aren't reasons for you to say "Hey! I think this might not be Antivirus!".
We can't uninstall the problem. It asks for the password. We don't know that.
Also completely normal. That's a standard feature to prevent users from turning off their protections in order to regain the performance they lost - and, incidentally, to make it harder for attackers to turn off the Antivirus to evade detection.
We can't stop this process. If we kill this from the task manager it restarts again.
Again, completely normal, for the same reasons.
I have a suspicion that it might be monitoring all of our actions like every keypress (keylogger).
Nothing you've indicated so far suggests this - keyloggers are usually far less intrusive than Antivirus programs.
We use this laptop to access our personal emails, facebook, bank
account. It will be a great violation of privacy if they are
keylogging or somehow managed to monitor our SSL communication like
HTTPS websites skype, facebooks messages
Depending on your location, it would be a violation of your privacy, but might still be completely legal. In the US employers have the full right to monitor anything you do on the equipment and networks they provide for you to do work for them.
...but I really don't see anything here that suggests that. Sounds like they just installed Antivirus.
Is there any way to be sure of if they are doing anything like and confront them?
This question discusses detecting keyloggers, but the short version is, "not really."
This question discusses detecting corporate MITM, which usually boils down to examining the certificates of sites you visit, and checking your computer's Trusted Root Certificate Authorities. This is relatively easy to detect; the modern (lovely) tendency to use TLS for everything increases transparency.