It must be gritty and drain well. There are bunches of options. Searches for "succulent soil mix" will give images of how they come out.

This is tricky. You either need to drill a drainage hole, or decant excess water to drain it after watering. In closed containers with straight edges, decanting isn't too bad. It becomes unworkable if they are curved. Avoid having walls of the container enclose the plant. They need good air flow.

Haworthias, aloes, gasterias, and hybrids, at least. If you have ways to get ample light to them, then anything you can fit. Sempervivum tends to do best outdoors in most locations. Stonecrop sedums do well outdoors as well, and I don't know how they do indoors.

Maybe. They can limit airflow and evaporation. Things like terra cotta pots wick out moisture from all sides and better handle top dressings.

Look over care in detail and find the subtleties for each plant you want to group. The more similar the care, the longer an arrangement will last before there are problems.

For most, when they are dry and in active growth. "Overwatering" is a bit of a misnomer for most species, as root rot tends to come more from drainage issues than water volume and frequency. However, pay attention with each new addition to water appropriately. An example of an exception is lithops.

Most encourage that you don't buy and save intentionally damaged plants, as it just encourages people to keep making them. However, rescue operations do often have success. Also, sometimes it's the only access you have to a certain species, and decide to make an exception.

Give them strong light. It's hard to give too much as long as you increase the amount gradually. They need good drainage and airflow, particularly in humid areas. Most can't handle freezing temperatures. Keep hanging out on this board and similar ones, and let the information trickle in. Don't overcollect. Take them in at a rate that you can learn about each, unless you stumble on a great deal. Propagation is fun.