This depends on when you wanto travel. During the summer months some huts are near impossible to book last minute. So if you’re planning a summer trip along a popular route such as the Walkers Haute Route or the Tour of Mont Blanc you need to be booking in the autumn prior to your trip. These days it’s all easiest via the web.
Wild camping isn’t allowed except in an emergency. To help save the fragile environment in the Alps you will find that Guides and IMLs use huts wherever possible.
Yes, depending on where you are going. A Reciprocal Rights card can get you a discount of between 20% and 50% in many huts. Find out more.
AMS stands for Acute Mountain Sickness. It's a collection of symptoms that you get from going too high too quickly.  Find out more.
A good initial source is the useful download booklet by Medex called Travel at High Altitude

There is some information that you might find helpful here

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