HIGHLY recommend going to a decent tandem retailer - if you're in Wales, your best bet might be Peter Bird over in Ironbridge -
http://www.tandeming.co.uk/My better half and I went and hired a tandem from him when we were considering purchasing one. He spent an hour or so showing us how to ride a tandem (there's a few things that are a little counter intuitive). He was superb and explained all the basic principles.
OK - you have a lot of questions:
Size difference - not that an unusual pair and I would have thought you'd have no problems buying off the peg. It is certainly easier with the stronger rider up front, but by no means compulsory.
pretty much every other question you asked - EVERYTHING on a tandem is about communication and compromise
You will not move at the speed of the fastest rider, nor that of the slowest - you'll find your pace somewhere in the middle (if you try and tear her legs off, you won't be tandemming for too long!).
Climbing hills on tandems is, typically, a fairly slow process compared to a decent solo rider - low gears, spin away. On the flipside - downhills and flat bits, without too much effort you should be quicker (especially downhill where things get very fast, very quickly).
Typically the rider up front deals with gears, steering and braking. The rear rider will deal with signalling, looking around before manouvering etc. So there's a lot of trust in both directions - up front, I have to have absolute trust in Cass if she is telling me it's okay to move lane etc. and she has to trust me not to steer us into a ditch.
Gear changes - you will call them a lot at first (and this is a good thing) - nowadays, neither of us say when we need to change up or down a gear, we just know. We still tend to call front ring changes though.
Overall tandem experience - best way possible of cycling with someone who is of different pace/strength to you - no waiting at the top of hills, no being waited for. Lots of talking. Some bottom fondling. Lots of attention wherever you pull up for a stop!
They are fabulous things - take trust and communication - but if you can do it (and some couples just can't (and I don't think it has anything to do with the strength of their relationship or any subtext like that)), then you will never have more fun on a bike than riding on a bicycle made for two.
And the golden rule? The stoker is ALWAYS right. Follow that and your life will be easy.