|"Could a person get a something like that if they were lured to|
a fake websit & gave a password for a game site on this fake
Well that is a different kind of hacking which we call Social Engineering or Phishing. Some one who pretends like they are a Systems guy asking you for your password. Just NEVER EVER give out your password or login information. If they are a sysop then they have access to the database and could simply reset your password so they will never ask. The same applies for personal information like social security numbers. If some one asks see if they will simply except the first 5 numbers. Last 4 is over used.
You may think I am a security freak but I never buy anything online unless they have a certificate from a certificate authority and I never ever by things over the phone with a credit card because those under-payed phone jockeys on the other end can take the information and use it. If you cant do it on a computer or in person then don't.
"Also, would the free verson of this malwarebytes be able to remove it if I did have something like that going on my "
Not 100% guaranteed because once someone has access to your system they can install keyloggers or other custom made systems or even worse they could put in some rootkits that can hard to be detected by a virus scan.
If this ever happened to one of my computers I would simply re-image back to a time before the misidentify but I am guessing you don't keep disk images of your system.