These issues can take time to diagnose. If you're able to connect remotely with a Support representative they are likely to be able to help you in a more timely fashion. That being said, the first thing you will want to verify is resources:
If your LEM deployment is under powered for what you're trying to do or your resources are not reserved, then you're going to run into plenty of issues with slowness.
Additionally if you are able to get into the console, you will likely want to disable all rules (and be sure to Activate Rules) until you can diagnose the issue. If you have a lot of active rules (or a few that are very active) then you want to get these disabled so that you can tune them and work out from there.
For additional reading:
After the above, I decided to install a fresh VM for LEM. So, I downloaded a fresh copy with the same version 6.3.1 and disconnect the old VM and connect the new one. I uploaded the configuration file of the old VM to the new VM and hoped that this will work. But wasn’t the case and the agents weren’t discovered by the new LEM Manager.
I decided to return the old VM and accept the slow performance. BUT the issue that all the agents now are discovered but all of them keep connected at 12 September without any update. Also, the slow performance is gone and it is perfect now as no logs or communications is done between the Manager and the agents. When I try to install a new agent on a new machine that wasn’t discovered before, the LEM manager discover it but as disconnected agent with last connection date as “16:00:00 Wed Dec 31 1969” which is very strange
Any advice why this is happening
There are several moving parts here. It's going to be the most efficient use of your time to reach out to Support.
The bulk of your current issue appears to be certificates. Your agent reporting from 1969 likely either didn't get all of the certificates, or can't connect fully to the LEM. The existing agents you will want to clear the Agent Certificates.
If you have many agents that would be difficult to touch directly then Support should be able to assist with this.
You can't set up a new LEM and expect the nodes will connect to the new appliance without any additional configuration due to certificates tying the agents to a LEM deployment to specifically thwart this type of scenario.