It is not only when the synaptic potentials arrive but where the synapses are located on the target neuron. Spatial summation occurs when two presynaptic neurons are located at close enough distance that their individual inputs can summate. Having NT permanently bound to the postsynaptic receptors would cancel the ability to communicate additional messages. The most rapid system is via enzymes. The NT acetylcholine is an example.
Reuptake is via a carrier-mediated process in the presynaptic neuron.
A certain amount of all NTs will diffuse from the high concentration cleft to outer fluid. For some NTs this is the major mechanism.