probably the axle is longer than the dropout, so the bolt is tightening up against the axle instead of the frame, a quick fix would be to pop a washer over the axle between the hub and frame, the better way would be to file down the end of the axle slightly. both will fix your problem.
the skipping feeling may have been your axle, but it was more likely the chain was too long like your friend said, if you managed to get 3 links out that deffo sounds like the case! the position it's in now it fine, but you could remove the pin behind the main bolt thats pressing against the hanger, this will allow the tensioner to sit even closer to the frame increasing the wrap around the rear cog.
Edit: Just seen the other pics, you should deffo get the tensioner closer to the frame as I mentioned with removing the pin, and there is still room to get another link out of that chain I should think. you should also try and have quite a lot of spring tension if possible.