I'll answer some question, in no particular order. The other reason Ruin picked Vin was because Preservation had already chosen her, and by spiking her he thwarted his old enemy's plans. For a time.
I believe the mists were reacting to both the well and to Ruin, both of which were particularly active during those time periods. Ruin had a spiked pawn at both times, and the well was full. I assume that's what the mists were up to.
Note: Don't forget the Lord Ruler. It would have been within his power to shove the mists backwards power-wise, but probably not for long.
For Kelsier, there is either a yet unknown way to drop a shard or already being dead allowed him to do so.
I think he could talk to Vin and Spook because, like a Scadrians, he had a bit of Ruin in him, allowing for mental communications.
Elend pushes on coin, making it weigh his 200 pound plus an extra 100 or so thanks to his power. Inquisitor only does 200, and as such Elend takes the stumble from the Inquisitor's 200, and the Inquisitor takes the hit for the remaining 100 he didn't cancel.
That's all I've got for now, but:
*Terminator voice*
I'll be back.