I've not flown on British Midlands, but I am under the assumption it is similar to the cheaper intercontinental flyers of the past (Air Transat, etc) and so I would say that.. You get what you pay for. If you don't mind being packed into a smaller airplane and them skimping on a few corners, then they are fine. British Airways is very similar to AC.
Book your flight to Ireland when you get there, using either Ryan Air (
www.ryanair.com) or Easy Jet (easyjet.com)... The trick to using these airlines is to fly Monday-Weds as their weekend rates are double and sometimes triple what you'd pay on a Monday, Tuesday, Wednesday.
Travelling into France/Germany... The most convenient way would be to take the Chunnel from London Waterloo station to Paris (or Lille) but it is rather expensive. As I recall it ran me close to 50-70 pounds ($150-175 Cdn). You're best bet is probably to find another Ryan Air or EasyJet flight.
Once your on the continent, then I would say, if you've only got two weeks, buy a Eurrail pass (
www.eurrail.com).. If you are only going to do France/Germany then I would buy the Fr/Ger regional pass, and, depending on how many places you want to go, you can purchase a pass with 4, 5, 6, 8 or 10 travel days (i.e. Paris---->Frankfurt = 1 travel day)
Flying on the cheap airlines is not any quicker (or much cheaper, actually), once you factor in transportation to and from each airport (they are always located at least 20 and sometimes up to an hour outside of the city you are flying to) and airport delays (checking in, etc). They are great for getting to and from the UK, and flying long distances on the continent, but its not really worth it if you are staying in a confined area of France/Germany.
Not sure about the passport thing, but hope that helps you.
EDIT: Just wanted to mention, travelling by train is also a great way to take in more of the country side and give you more of a "travel" feel... It can be a bit monotonous shuffling from airport to airport. Trains also allow for greater flexibility of your schedule, with trains on major routes running every hour.
And whatever you do, don't bypass Berlin! One of the greatest cities in Europe.