I've found that whenever I climb in either the early Yak's or Spitfires, I die much quicker and get less kills. It usually goes like this:

Then you are doing it wrong. Altitude = potential energy. Yak is energy fighter.

1) Climb to either 4km for the spitfires or 3.5km's for the Yaks

That's good. But keep in mind some planes perform poorly the higher you go.

2) Go into head ons with 3/4 aircraft because I'm the only one there. In the Yak this is a blessing, but even then you can get hit by a lucky shot and die.

That's your issue mate. Learn to avoid head ons. Watch RAMJB video where he explains how to do it.

3) I can turn all I want and some of them will turn with me, but the thing is that no one else has climbed with me so I'm the only one there. If I do get them to lose altitude, it just leads to my team getting the kills. And as much as you can bang on about "Situational awareness" it's hard to keep aware when you're fighting 3/4 aircraft on your own, and one lucky shot can either kill you or disable you.

That only prove your team is full of idiots. You can also try to drag enemy down.

4) I get shot down or get fewer kills than I could get.

Sounds like you need to learn few things.

Would it not be better to stick to flying at 2/3km? That way when enemies dive on you you have much more time to dodge, and they have to burn all altitude to get at you and it's easier to dodge them if they're going at 300/400 kilometres an hour. Not to mention you're less likely to be targeted if down below. Could some people experienced at turn fighting tell me which one to stick to?

No because you are making yourself an easy target.

Edit:

Also whilst on the point of turn fighters, any ideal speed to turn at? Should I be as slow as possible or at some other speed range?

It really depend on plane. Each plane turn better at different speed.