Yes, all the alarms to be interconnected must be on the same circuit. At least, that's what I recall from installing my alarms. 14-3 works well for wiring in smoke alarms. Use the red as the signal wire.
Technically, I believe the code says they should be on a circuit that also supplies power to an essential light, such as a hall light fixture. Thus, you'll know if the breaker has tripped and be less likely to simply turn the breaker off to silence them.
A candle or two should not set off a smoke alarm unless it is burning directly under it. Read up on the various types of detectors and their placement and make appropriate choices. You can buy detectors with a "hush" feature which will turn off the alarm quickly so long as the smoke or fire detection doesn't persist.
