Where in the nervous system are synapses chemical, and where are they electrical?
Synapses are almost all chemical, the electrical synapses are more of a "special case".

The speed of transmission across limbs, etc, has very little to do with the speed of the actual synapse. The signal itself is conducted electrically inside a given cell (this is an "action potential"), aided in many cases by insulating myelination. The synapse is just the endpoint.

Some places where electrical synapses/gap junctions are present are:


Between cardiomyocytes, to synchronize heart contraction
Between certain networks of inhibitory interneurons in the CNS
In some (but not nearly all) reflex circuits