1) What's likely to happen if I attempt to bend the mast back?
It depends on how badly the mast is bent in the first place. If it's buckled, forget it - it's toast. A gentle curve can be straightened with no ill effects.
2) Were I to attempt to bend the mast back, how should I go about it?
The best way that I know of is to find two stout trees about 4' - 6' apart. Strip the mast bare of everything that can easily come off. Thread the mast between the trees, and with a helper holding one end, position the mast so that the apex of the curve is on one tree. Pull on the other end (you'll be surprised at how much force it takes) to work out the bend. "Bouncing" the mast may be necessary to work out the bend. Work slowly - don't try to take out the bend all at once. Sight down the track often to check progress. The trees naturally spread out the force so that the sidewalls don't buckle. You will probably have to shift the mast position several times to get it straight.
3) What did I likely do wrong in the first place to incur this bend? (The boat hasn't been sailed in super-heavy wind, and has only a single trap rig, so it's not as if we have been (or will be) putting usual loads on the mast. We did have one stuck-in-the-mud turtling incident the first year we had the boat, which is what I've been blaming in my mind...)
That is probably the reason. Another cause can be sailing with the mast counterrotated, or having the boat flip over on the beach hard (like in a storm).