1. 30 minutes is a significant number. There are other timeout settings besides the two you listed that will affect this. There is an IIS timeout setting for the QvAjaxZfc application. I think the most likely setting affecting you are the QMC System -> Setup -> ServerName -> Performance -> Maximum Inactive Session Time and Possible Session Timeout, both of which are set to 1800 seconds (30 minutes) by default.
Document timeout is unrelated to user session length. It determines how long the application sits unused in RAM on the server until QVS decides it's safe to flush it from cache.
2. There is not generally a communication problem between QV and IE.
3. You can't control the timeout within IE. The timeouts are occuring on the server side.