They want your passport and will need it to put the residence card in. I specifically asked recently whether one could send a certified copy instead (and submit the passport at a later stage when they are finally ready), but was told that this was not allowed. Apparently, some people have managed to do this, though.

No - it is definitely possible to travel outside the UK while your application is "under consideration". It is your express right - as outlined in the EU Directive 2004/38 - to leave the UK and return (both EU national and non-EU spouse) whenever you want. Once you have submitted the passports, you can ask for them to be returned if you need to travel. This has no influence on your application process. Although the Home Office/UK Visas doesn't particularly like the idea, the reason for travel does not have to be an emergency.
If the Family Permit of the non-EU spouse has expired, the Home Office and particularly UK Visas insist that a new Family Permit has to be applied for in the country to which you are travelling. If this is no problem, this is probably the easier solution; however, the EU directive clearly states that no such document is required to exercise a treaty right (e.g. to enter the country whenever you want) - that's for example in Article 25/1 of the EU directive or also in 11/4 of the UK Immigrations Regulations (2006): http://www.opsi.gov.uk/si/si2006/20061003.htm. So as long as you two travel together and have the necessary proof that you are indeed married, even the most reticent UK immigration officer should at some stage realize that they will have to let you in (unless, of course, you are a known terrorist or have one of the very few qualifying nasty illnesses that count as reasons for the refusal of entry).

If I had known all of this 4 months ago, I would have had a different summer...
Good luck!
Sebastian

 

As EU citizens do not need a passport there is no need to send it in if you have one.
The ID should do, in my opinion a certified copy.

If they want the original and keep it for more than 5 days (the period nationals normally receive their ID or passport), do send a complaint to the European Commission.