I also think you may need to pass your writtens in the state your training in.
No, you can do the written exams in any EASA State. Bare in mind each State sets its own exams so the format, content and language will differ. The Irish CAA has refused to accept UK exams because it believes they may be compromised. PPL Confuser et al.
I agree that 10 days is short for a good comprehension of the material, but many have passed the exams in that period. I recall one student not so long ago who had sat and passed the ATPL theory exams prior to doing his PPL, the school said "but he doesn't know anything"!
There are a few schools who advertise ground school, Google them and ring around. Make sure they are an ATO or DTO and that you will get a course completion certificate along with proof of their authenticity. All exams must be passed in the same State.