My wife and I are planning a week long hiking trip to an area full of scrambling, sheer drops, and unpredictable river crossings. We've done this route before, but at the time we didn't have any preparations in case of a fall or a hazardous river crossing. It seems like a climbing rope would be handy for a rescue in any of these situations, but what we are really lacking is experienced advice.

There are a few main situations I'd like to prepare for:

1) while scrambling, one of us slips and slides down the mountain. I'd like to arrest the fall if possible, and recover whoever fell.

2) one of us looses our footing on a sheer ledge (no more than 30' high) and falls or slides to the bottom. Again, I'd like to arrest the fall if possible. More than likely though, whoever is still on the ledge will have to come down to the injured person and offer aid and recovery.

3) While managing a particularly nasty river crossing, one of us looses our footing and gets washed down stream. How should we tie or hold a rope between us to prevent or recover from this situation?

I have a few major questions, and I welcome any tips on things I may not have considered.

Question 1) Should we have some sort of climbing rope connecting the two of us on difficult parts of the climb or the river crossings? If so, how? It wouldn't be hard to tie a hasty harness and run a rope through a biner during those parts, but I really have no idea what would be best.

Question 2) Assume one of us has fallen and is injured. The uninjured party member needs to get down there to help out. Would a hasty rappelling rig need to be made? If so, what can I use as a hasty anchor if an obvious tree isn't available? What might I need to do to get the injured person to a safer area?

Question 3) I'm on a steep slope or a sheer ledge with minimal footing and I begin to fall. What can I do to minimize injury?

Question 4) What is the safest way to cross a river as a two person team with a rope?

Question 5) With all of these concerns in mind, what types of basic gear should I carry? What type of rope would suit my needs, and what length? What can I use to make a hasty anchor? I'd rather tie my own harness than carry dedicated ones (unless a pre-made harness is lighter). Do I even need harnesses? Is there a specific type of carabiner(s) that would be considered essential? Price and weight are concerns, but this is primarily safety gear so I'm willing to carry whatever I need. I'll carry a chevy on my back if it means that I can keep my wife and myself that much safer.

Background: I'm not much of a climber. My experience is limited to some indoor walls and some military rappelling. I love doing it, just haven't made it a full time hobby.

- Just connecting two persons with a rope and thinking that one might stop the other persons fall is a very very bad idea. You will just end up with two people tumbling down the slope.
qwert

That's what I figured, and is exactly why I'm researching the matter.