Actually, I just have better things to do on a Sunday than sit here talking to a wall.
Your knowledge is wrong. In nature the second heaviest hydrogen isotope, deuterium, occurs naturally, from either the Big Bang or other stellar activity. So, yes, there is "pre-fused" hydrogen when the brown stars forms. Brown stars can only burn this isotope as their mass is insufficient to burn the lightest hydrogen isotope. This is my point. Brown stars have little fuel that they can burn. See table 1 of www.lpi.usra.edu/books/MESSII/9038.pdf , less than one part in 1000 in most cases.
The hydrogen atoms were fused from within the star, earlier in its life. It's part of the process and life-cycle of the star. The fused atoms didn't just appear from nowhere. They occurred from that star's stellar activity. In order for the second stage of Stellar Fusion to occur, the first one must occur. It occurred early in that star's life of becoming a star, but it's still part of the overall process for the life cycle of those atoms in that reaction, which is why I said that the process encompasses both steps of the proton-proton chain reaction.
Again, wrong. You've forgotten that the internal convention will continue to heat the surface. If you understood, Newton's Law of Heating, you'd realize that the rate is dependent on the surface temperature. So, it's either cold (already radiated) or still losing the heat at a significant rate.
Bodies don't cool at a significant rate in space. Haven't you been keeping up with NASA's fiction over the years? They go on and on about how heat loss is a major problem in space. It's one of those "amazing facts" they teach grade school children with. The story goes that it is very difficult to get rid of heat generated by instruments in manned and unmanned ships. They say that the Space Shuttle has more issues getting rid of heat than it does trying to stay warm, which is why it flew around with the bay door open.
There is a short story by Frederik Polh called "The Mapmakers," that works on this general premise; a starship, unable to navigate to a planet to obtain air as a coolant, is slowly dying of increasing temperature as it can't rid itself of its own waste heat from internal processes.