It`s all down to the way the magnetos are "timed", if you don`t start the engine on whichever mag the "impulse" is atatched to (can be either, usually the left) you can do damage!
Not necessarily. You may have a harder time starting, however. Some engines using an impulse coupling make use of both magentos for start, and some don't. Engine damage is seldom the issue at all, but ease of starting is.
Magneto timing takes place in two ways. Magnetos are internally timed to what is known as "E gap," and are also timed to the engine. Both affect the operation of the engine.
Magneto-to-engine timing is the timing to which one generally refers, and to which you are referring; it may be fixed or variable, depending on the system in use. Most traditional magnetos use fixed timing at a set position before top dead center, and some use an impulse coupling or a shower of sparks system to set up a spark advance at low RPM's, or a series of sparks at low RPM's that blanket the advanced position to ensure a lightoff close to top dead center.
Not all engines utilizing one or the other will require a mag shut off for starting. Refer to the aircraft flight manual or operating manual for specifics. Even aircraft of the same make and model, but different vintage or different engine installations may have entirely different procedures; make sure you marry up your procedure to the specific airplane.