A passport is not necessary ONLY if you are an EU National and travelling between EU nations. If you are a non-EU National, you cannot travel without a passport. Any immigration / border patrol officer in any country is in no way required to allow you in with the documentation you stated.

 

As your legal stay is dependent on your wife's, you'll get a card that is valid as long as hers.

Theoretically they should allow you in without a passport (is the conclusion from the Brax/Mrax ruling of the EU court) and practice over here in The Netherlands. The only requirement is there should be no doubt about your identity.

However, no airline will take you without a passport. So get it back a.s.a.p.
Directive 2004/38/EC does not allow them to keep your passport. And national UK law cannot make such a regulation, though they probably think (mistakenly) otherwise.

 

It has to be valid for 5 years, unless they have evidence that you/your spouse intend not to stay that long. The foreseeable end of studies is no such evidence (because you can obviously stay and get a job), and usually the Home Office understands this and will grant the full 5 years.

Yes, they should do this, and they probably will. If you are both traveling together, it will probably cause a short delay, but I cannot imagine that they would refuse you. If you travel alone for some reason, it could be a rather risky thing to do, because you also have to prove that your spouse is already in the UK.

One last point: if you apply for EEA1 and EEA2 together, the applications should be processed together within about 2 months, well before Christmas. But if the EEA2 application is processed separately, it will very likely take 6 months, and you should allow ample of time for them to send the passport back.