I don't think you'd be able to hook that pump into the computer power supply that easily (perhaps if you ripped it open you'd find it runs on a 12V motor or something, but it'd be a lot easier to just plug it in regularly).
And well I don't know much about mushroom farming so some of this might be a little off. But I'm guessing you're gonna need to test the air humidity. The moisture content of your soil, and the temp.
Then based off of those youll trigger the mister and the fans to keep the moisture and temp at the happy place correct?