Hi OP lots of good advice here.
I would suggest in regard to holidays, a good time can be July, as school and exams are done but results day is not for a while. Also you can sometimes get a good deal (assuming no other children in school). But yy, check with your DC's school about prom - the timing will vary and they may not want to miss it. Prom is often in early July (but some schools have it in May).
To answer your questions:
GCSE exams start in early-mid May and run until end of June. Exact dates depend on subjects (but not on the board! all Maths GCSE exams are on the same days). If DC is taking MFL, the speaking exam will be in April-May. If they are taking art, the exam is in the spring term I believe. Both of those will be on a school day tho.
Students sitting 9-10 GCSEs will have a lot of exams so may well have two on one day. Or even three sometimes (less common with GCSE than A level). My DS had 10 exams in his first week.
Study leaves varies - check with the school. Many schools start it at May half term, but my DCs' school encouraged students to come in for relevant lessons after half term as well.
Mocks vary hugely so no one can help you there. School I worked in they were in November and February; my DCs' school, December and March.
In general, I would avoid any holidays in year 11, certainly anything longer than a short break after January tbh.