Can the cannons be used as turn signals with most vehicles? Yes, as long as there is no canbus system that throws a fault for turn signal out. Even then if you are creative and saavy enough, it is possible.
Do they require a resistor to function normally? define "function normally" if you mean no fast flash from the vehicle because it is detecting a bulb out then yes. You will need a way to equalize the load on the vehicle so it doesn't think that the difference in amps used between your stock bulb and the cannon is the result of a bulb being out.
Can you sync single color Cannons(2 different colors master/slave) with dual color patterns on the Apollos? Yes, as long as they have the same firmware.
Can you sync dual color dash lights Apollo/Cobra with dual color surface mounts? Yes, but the T3 and wide lux will only synch with the apollo/cobra line on certain flash patterns. The T-6/F-6 and cannons should all synch together fine as long as they are of the same firmware.