Hello Ramah,
thank you for your interest in Test Studio.
Yes, Test Studio can be integrated with TeamCity as described here:
http://www.telerik.com/automated-testing-tools/support/documentation/user-guide/command-line-test-execution/continuous-integration/teamcity.aspx
You state:
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:
http://www.telerik.com/automated-testing-tools/support/documentation/user-guide/knowledge-base/test-execution/no-tests-execute-on-locked-machine.aspx
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:
http://www.telerik.com/automated-testing-tools/support/documentation/user-guide/knowledge-base/code-coverage/using-ncover.aspx
I hope this helps.
All the best,
Stoich
the Telerik team