I can only answer from the standpoint of renting points FROM someone, not renting my points out.
The reservation gets made in the name of the renter.
You should work it out with them in advance - what do they want, resort, dates, room type, etc. Then I would say tell them if it's available, you will book it. If they want to give you multiple options and you're checking on all of them, then obviously you would have to call them back and see what they want. I would make it clear that availability can change minute by minute though.
As for them taking another offer, hopefully they wouldn't be accepting offers from 2 owners in the amount of time it takes you to check availability and work out your deal -- that would be bad form. It should only take a few hours or even minutes.
You can always cancel without penalty as long as you're not within the penalty periods (30 days out or less).
Again, you can probably get better advice from someone who rents out their points frequently but I wanted to offer what I know.