rogerk8 said:
I know so little and understands so little so maybe I should quit now?
Anyway here is how I see it:
F_G=G\frac{m_1m_2}{r^2}[N]
F_Q=\frac{1}{4\pi\epsilon_0}\frac{q_1q_2}{r^2}[N]
where for protons
m_p=1,67e^{-27}[kg]
G=6,67e^{-11}[Nm^2/kg^2]
q=+e=1,6e^{-19}[As]
\epsilon_0=8,85e^{-12}[As/Vm]
which gives
\frac{F_Q}{F_G}=10^{36}
This clearly states that, in the beginning, protons could not have bundled up due to gravity while the electromagnetic force is way much higher (to say the least).
So far, so good, in the Newtonian sense. However, as Drakkith noted, the sun is electrically neutral, and started from Hydrogen atoms (and other stuff). By the time you need to worry about proton repulsion, you already have the 250 billion kg/cm^2 pressure of neutral matter above to overcome it.
Now, for the more remarkable GR correction to the Newtonian picture (though this is not relevant to the formation of stars). Suppose you put one proton in a cubic meter of vacuum, building this pattern out. According to GR, there would come a point, as you built this outwards, where this framework was within its Schwarzschild radius, despite the ultra-low density. Then, no matter what, the assemblage would collapse to a singularity, no matter what forces applied to the protons. The progress toward the singularity would be exactly mathematically and physically equivalent to the progress of time, so even forces approaching infinite would not be able to stop the collapse. Thus, per GR, enough stuff, however sparse, must collapse - if you have enough of it.
rogerk8 said:
So what happened? I see two scenarious:
1) The first particles to bundle up was neutrons and when they bundled up tight enough they somehow mutated into protons which after a while where able to fuse into He_2.
No, much simpler, it started as Hydrogen atoms.
rogerk8 said:
2) Reading your kind answer makes me think that perhaps the first neutral (which is a must here) particles where neutral protons i.e pure H_1 which later fuses into He_2.
Correct in that the starting point is Hydrogen gas. However, the fusion reaction is not to Helium 2, which would not release energy. It is to Deuterium when the proton-proton interaction is accompanied by emission of a positron and a neutrino. This process releases energy but is very rare. The further steps from here to Helium 4 occur and much higher rates and release much more energy.
rogerk8 said:
Now I will try to answer your question "How many times more massive is the sun than the moon": I have no clue

To me the sun is of course massive but it is also gasous like a plasma, right? So, stupid as I am, I would actually consider the moon to be more massive than the sun because it is made of dirt, so to speak. Please, educate me some more here if I'm wrong.
Roger
PS
I kind of know how to write isotopes but I fail using <sup>.
The core of the sun has a density of about 150 grams/cm^3, well over 10 times the density of the Earth's core. This is because of the enormous pressure of the overlying layers squeezing an ionized plasma to a density beyond any material we know on earth.