Well, if you need anything write at my ICQ (pm for it if you want) I am programming in C++ quite... first you should try to make some really stupid, but simple apps. Don't mean making hello world stuff again and again but working with classes, fields etc.
for those you don't need any engine...
get VS 2008 Express C++
http://www.microsoft.com/express/download/#webInstall
Then get some nice book.. try searching for:
- Learning C++ in 21 days
- Thinking in C++
There is also one great publication "Mistrovstvà v C++" but it's in Czech so you probably won't read (maybe it's somewhere in english I don't know saw it only in this version, the exact transl. is "Mastery of(in?) C++" )
When you got one read it all and make their exercises. I don't want to say anything on online tutorials but if you take book and tut you will see difference on your own

At least, it's paper and you don't have to switch windows
To the questions for Solurus, I'll answer from my view:
1. No, but I tried (succesfuly) modify Freespace 2 code
2. I would write my own because my first game will be really simple and engine would just blow my mind away
3. If you take my age of 16 the answer NO is reasonable, but I'm looking forward working in those areas

But wahtever I built my very own calculator which got much of improvments and can not be compared with windows calculator (for more pm me I'll maybe share you some code for educ. but it don't lie within this topic much)
4. The question is .. for what:
- DirectX for Windows for sure
- OpenGL for anything else
Note that you can build OpenGL apps for windows too but DirectX is just too great
5. Well there are non.
Not because I don't know about it but it doesn't fir in anything I made for now. Lancer, if I can, I'll correct you. You don't need math, you need the formulas from physic mainly. The computer will compute everything, BUT you need math at second place surely, because all programing is about algorythm and those are areas of logic -> math. So well you need to know all 3
Then it's just easy to make gold ball and use:
m = Ro * V
F = m * g
And you get the gravitation force. You'll just specify constants and set your only value, the volume (which can be again calculated with math formula from radius

)
So if you want help pm and I wish you all good. Happy playing with C++
