The execution server has the option to Run on start up, which you have enabled. With the current implementation we try to start it like an application with name Telerik.TestStudio.RemoteExecutorfor.exe for each user that logs in the machine. This is why you see the error message when you log in with another user. In case you encounter the same error in a different scenario, please share more details about the environment and steps to reproduce it on my end. I will then be able to analyze it and try to provide a solution or report a bug on your behalf.
You can execute test list locally or remotely, via the scheduling service and the execution server even if it is on the same machine with Test Studio. The remote execution requires you to have scheduling and storage servers and an execution server that is connected to those. You could use multiple different accounts to access Test Studio, as far as I know, and run your test lists locally or remotely, if you have configured scheduling and storage services and connected to them.
When you disconnect your RDP session, we use the TSCON Windows utility to connect your session to console. The problem appears to be that in that case the resolution of the console sessions falls back to the default resolution of the virtual machine which in your case appears to be too small. Since you mention that you have a working solution, I would suggest to keep using it until we manage to provide a built-in solution of the problem. You can follow the public bug report, which I created on your behalf.
I hope you will find the above information helpful. I remain available to continue our discussion.
Thank you for your valuable feedback. As a token of gratitude, I have updated your Telerik points balance.