I believe it should be accepted as well, it isn't just used for the current state but also for permanent traits depending on the context. Eg, If you move to a new school, your friends may inquire about your new classmates by using "How are they?" meaning the same thing as "What're they like?"
No. It's not the same thing. 'What are they like?' Is a full thought than can be answered.
'How are they' is really 'how are they...' and the receiver must then fill in the rest with context. So your example is something like 'How are they [as far as their acceptance of new students]?' Or something like that.
Yes and no. It normally means how are they doing. Some (mostly british) use this to mean what are they like but it's a very common mistake for people to make in english as a 2nd language to say this and mean, what are they like.
Using how are they in the way you mean really is just an imcomplete thought. It's more like 'How are they...[to be around?/as far as ability?/etc'.
You could argue this but it would introduce a lot of confusion if they accepted that.