All of those answers depend entirely on what level you plan to compete.
All of the stock horse breeds (QH, paint, app) are hghly favored for western pleasure. Morgans, arabians, saddlebreds, and tennessee walkers all have western pleasure classes as well. And the ideal standards for those are all breed-specific. An arabian should be different from a quarter horse, for example. So really, you could ride just about any breed of horse in western pleasure. But that doesn't always mean you'll be competitive, as not all horses are suited to the event--just like not all horses aren't suitable to be jumpers. I know my western pleasure horse would probably break her neck trying to bet over a small fence!

I'll give you the generic standard for a stock breed western pleasure horse: the horse should be slow, collect, and relaxed and perform all maneuvers on a moderately draped rein; should exhibit three clean gaits (four beat walk, two beat jog, three beat lope) and be able to extend and collect those gaits on command; maintain a headset that is natural for the horse, althought he favorable headset is to have a level neckline (poll even with withers) and head slightly past the vertical; horse should have smooth transitions; and have a pleasant expression. Remember, the orignal intent of the class was to show that your horse was truly a pleasure to ride--a nice slow, relaxed, collected lope can feel wonderful!
AQHA put out a few videos in conjunction with Alex Ross that would be EXCELLENT for you and your trainer to watch. One details selecting the western pleasure prospect and judging the gaits. The other was put out about 5 years ago and was sent to all the judges to remind them what to look for

I own the Cleve Wells video series, and they dovetail nicely with my own training program, and I've heard very good things about an older book by Doug Carpenter.
I personally love my western pleasure horses, and use the event as a basis in training from which I expand their repertoire. A well-trained pleasure horse knows all the basic skills needed to progress to horsemanship, western riding, and trail. I would think that your dressage teacher could probably do fine learning western pleasure, although it wouldn't be a quick transition. The feeling of a western pleasure horse and a dressage horse is very different.
If you have any other questions, please let me know. I think I'm the resident western pleasure junky

Oh, and if you want to wear a helmet then go ahead. You're hear no tut-tuts from me.