Yes - You can change schools.
As advised make a decision based on all the facts (particularly rapport with instructor and school reputation, not simply cost). Cheap/ better value doesn't always mean better.
Current school will have to keep your original notes with them (CAA inspection), but should photocopy them and then send them direct to your new school. Most places tend to not pass notes or copies to the student in case stude tries to amend them (particularly relevant if stude as had a major incident!). In the event you'd taken any theory exams they should also forward details of passes and provide you with a ppl application form witht he relevant theory exams signed off.
If you move schools and existing one won't play ball, new one should make contact (ideally in writing) requesting notes on your behalf. If they still refuse contact the CAA. A good school would also normally provide a brief covering note to go with your records.
Try to keep any decision amicable, afterall its a small industry. Not a plank driver so can't advise re the different types.
First flight with new school will more then likely cover new aircraft famil. If you perform to a standard consistent with your experience continuing from where you left off shoudl not be an issue, you can complete a certain number of hours on a different type so long as the overall required figures are met and all exercises are signed off as complete.
Apologies for spelling and punctuation, but its been a very long few days. Not that I'm complaining
