if there's a build up of charges that means there's no electrical circuit/flow of charges, so all the energy will just be given off as thermal energy... thus just a waste of time.
and electricity only flows if it has a complete circuit so without the salt bridge there is no circuit so yes, the electron flow/ current will stop.
seeing how fast electricity flows i'd assume it'd be a pretty instantaneous stopping of the current, not positive though... physics people would be more useful for this.
Spot on, a very small amount of current will occur, but this only lasts a tiny amount of time, since electrons flow fairly fast, and electric charges exert very strong repulsion to each other (the charge displacement of the electrodes will be tiny).
After that though, there will be no reaction. No energy will be dissipated via heat (if done right), since the two species cannot react because charge is saturated at both cells. It'll simply stop [or rather, reach equilibrium, where the rate of forward reaction (favoured by electrochemistry) slows to a virtual stop at the same value as the rate of backward reaction (very, very, very, very slow reaction)].
Electricity does not travel through the salt bridge. The salt bridge simply supply the correct counter-ions (such as K+ and NO3-) to balance the flow of electrons in the two cells.