BJJ - Your two questions:

1. My brother is going to LIM (I am only going on the 500K run, so will not get there). He could not find a hotel there either. But found a nice guest house in Miraflores where the owner speaks English and will pick him up and return him for a reasonable fee. Unfortunately, he is now is NZ and I don't have the name of place. But there is a Central Reservations Tel. 4466895 that you can check with. Or try San Antonio Abad Hotel T 4476766 that has a shuttle. A drive may be necessary, but better 4-5 hours sleep than staying at airport.

In BOG they are not supposed to charge you a fee if you are leaving on same day. But I think you can (from what I have read) stay in the transit area - assume no checked bags. But may be difficult to get an agent to get you boarding passes. If you leave, make sure they stamp passport with date of arrival so you can prove when you arrived.

Please post this info after your trip as, I think, the biggest question for most is how to handle plane transfers at the various airports without exit taxes. And BOG is a main transfer point and many concerned with possible problems there. Thanks and Good Luck!