1. Yes. Although its likely to get me a stern talking to, you can install Dameware on servers with other applications running. performance might be impacted depending on the scale of your environment. Obviously you need to monitor for side-effects.
2. usually you can register a Dameware license 3 times for a single user. That should allow you to use on both QA and Production. You need to be honest however. If you are going to be using them both for production activities you should buy an additional license.