There has been enough proof that the Q team are what they say they are. However, you do have the freedom of disbelief.

The ultimate proof will be when the end-game is complete, which shouldn't be too much longer.. hopefully. One thing is for sure, we are in it right now.

As for "Trust Sessions": He had a job to do and he did it. Do we know the details? No, but they were implying to trust IN him, to do the job he was assigned. It was clearly NEVER to be the one to take down the corruption. Maybe because he was too public a figure, maybe they didn't want to screw up his chances to get back in the senate. Who knows! However, he wasn't as sleepy as you think he was.