Intriguing questions

Some things are guaranteed to exercise my mind because I don't know the answers, mainly because I'm too lazy to look it up on Wikipedia.
For instance, take the sun, imagine being a photon that is about to be blasted out into space by the sun. My physics tutor (and first boyfriend) told me nothng goes faster than 300,000km/second, the speed of light. Now imagine a photon on the other side of the sun which is about to be blasted out by the sun at the same time as the previously mentioned photon. When they both shoot into space at 300k km/s, relative to each other do they travel at 600k km/s away from each other? If so, they would never see each other again or be able to make contact again?
If we transpose this to the Big Bang, does this mean that the original material that was blasted out is travelling in all directions at the speed of light away from each other and so will never be able to observe each other? Not just red-shift Doppler effect but perfect invisibility? So much light and material out there in space is practically impossible to observe because it is invisible due to the speeds involved? Is basically 99% of space out there then simply unexplorable for us? Will in the distant future, due to the increase in space expansion (at an increasing rate), all galaxies be so far away from each other that they would not be visible anymore? Our radio waves would become too slow to ever reach them, let alone get any messages back from them?
Another issue, imagine your car's petrol tank. When you first bought your car and filled up, are there any petrol molecules in your tank now that have been there all that time?
Don't ask why this interests me. I'm just an Aspie.