Except for few gyms that obviously provide documents for dtv @
*****
baht up (and they make a living out of that), most of the school are looking for real customers/students. It makes sense they don't do refunds cuz their main goal is NOT to provide visas but to offer classes. If u need the documents then u can do a fast research on this page and you'll find plenty of places than will offer refunds as well
you surely can but first of all you should figure out while your application got rejected. Jakarta is known for being a friendly embassy so I believe there was a major issues with your application
op is from the uk, if you apply for a TR visa, the embassy will reject your application and keep the fees saying "you got a british passport which allows you to stay 60days visa exempt. No need to apply for a visa"