1. On some of the VMs, the VMTools are installed but then they VMtools will say that they are not running. It is seen through the vSphere client. Any explanations as to why the status of the VMtools would change?
I would suggest you to re-install VMware tools again after uninstalling it. if issue still persist restart mgmt service and check whether it shows up properly.
2. We are running RDP on Windows 7 boxes and they randomly disconnect? I have found discussions on this through Google, an d it seems a few people have this issue. But no one seems to have the answer. Any ideas?
Can you try what is mentioned in this thread Remote Desktop Keeps Disconnecting - Microsoft Community if you haven't tried it yet.