I can tell you that you definitely do *not* need to have your Human Performance exam done before your 1st solo (it's the easiest one, anyway, I got 100%).
However, there are a lot of (needlessly) strict schools out there who may make you do it before solo. It is not a legal requirement.
All you have to do, is (1) Have your medical certificate (2) Pass Air Law (3) Fly to a consistent standard to satisfy your instructor so he/she will actually let you do 1st solo.
Some schools have all sorts of extra regulations, like making you have the practical RT exam done before your Qualifying Cross Country is a common one, and all sort of ridiculous currency requirements (Cabair and Denham spring to mind)!
Meteorology is a separate exam... nothing to do with air law.
The exams are are:
1. Air Law
2. RT Theory
5. Aircraft General
6. Human Performance and Limitations
7. Flight Performance and Planning
I recommend doing them in that order.. because, for instance you need to get on with the Nav exam after 1st Solo because the cross country flights follow not long after and it can take a while to get your head around visual navigation theory.
I suggest doing the whole course like this:
1. Trial Lesson/Intro flight
3. Air Law
4. First Solo
5. RT Theory
7. First Solo Cross Country
9. Aircraft General
10. Human Performance and Limitations
11. Qualifying Cross Country
12. Flight Performance and Planning
13. RT Practical
14. Practice Skills Test
15. Skills test
That's the way I did it... by the way, I dont know what the age requirements are because I didnt have to worry about all that.