thank you for your interest in Test Studio.
Yes, Test Studio can be integrated with TeamCity as described here:
It seems that we can use Test Stuio with teamcity but only if a user is logged.
I assume you're referring to the fact that you need an unlocked desktop in order to be able to run a UI test. This is a known limitation to UI automation, check out the following article on the subject:
Code coverage is not included in Test Studio. You can use a third party tool to perform code coverage testing. For instance check out the following article which explains how to do code coverage for web tests:
I hope this helps.
All the best,
the Telerik team