Well, it's never explained but it seems pretty obvious to me (about the fax): Michael probably provided a description of her ("Has a woman looking like (description of Sara) checked in recently/today?") Remember he gave Sara an exact date for the rendezvous (June 3rd), so it's not like lots of women who look like Sara were going to check into that motel that exact day... (Despite Sara leaving the third bird behind when she escaped from her apartment, hence missing the info of date and town, and pretty much getting there on the exact date by luck).

About Mahone, I didn't really like the Final Break much, so I only watched it once like 5 years ago and I don't remember exactly how the plot went... But I'm pretty sure he first sold Michael out so he could have his FBI job back and all that bull, then he probably just regretted it and "redeemed" himself once more by helping Michael stage the whole parachute thing. I could be wrong 'cause like I said, I don't remember it all, but that's pretty much the dynamic they've been pulling off for all of the last season... Mahone's gonna betray the brothers, now he's not, but now it really looks like he indeed is, but nope, he's not and in fact has been scheming a plan with them all along... and back again.