I thought the 'GQ' was a typo till I saw the second one lol.
For your question, pretty sure all you gotta do here is look at your player availability page. It shows Jimmy GQ unavailable for weeks 5 and 16. While Kyle Trask isn't listed as availably at all this year.
My suggestion to you is to drop Kyle Trask and find a QB in free agency who is available to play weeks 5 and 16 or you'll most likely be stuck with a 'street player' for those weeks
Also, bye weeks don’t affect a players availability. If the player was available during his NFL bye week, he will be available that week for you. It’s not like fantasy rules. It goes off injuries