Monday seems fine for carmax...certainly less busy than Sunday lol.
As far as INQs, no need to complete the loan. As long as there coded right, its combined.
At toyota you could try emphazing you only want it submitted to TFS but obviously unless you go to extremes and get them to sign something to that effect they can send it out everywhere. I recommend you just not worry tbh if you dont want a mortgage in a year.