Under what condition, if any, can I reuse the rags?
Few people bother but you can wash them, just as with any oily cloth.
It's probably best collected enough to make it worth doing a wash so store them wet (see next point). If you add some washing soda to the water you store the rags in it'll act as a pre-soak. Then either handwash or put into the washing machine on a hot cycle.
I would not mix these rags with other laundry. It might be safe but it might not and you can't know in advance.
What is the process for prepping these rags for safe disposal?
There's more than one method. The simplest and perhaps safest is just to lay them on the ground (although many woodworkers will drape them over the back of a chair or something like that which is probably just as safe).
Not crumpled up the heat generated by the oxidation of the oil can't rise to the level needed to start combustion in cloth or paper.
Another is to store them inside a metal or glass container filled with water. I have a mayo jar near where I do my finishing. When full you just dispose of it with your household refuse.
You can also burn them. Few people do this these days for obvious reasons. But it was one of the standard ways of disposing of them in the old days, often in the shop's wood-burning stove.
Once that is done can they just be thrown in the trash or is it considered a hazard still?
Yes it's OK to throw dried rags and paper into the trash. They are no more a risk than printed magazines at that point.
And just like with paper you can also compost them. Even dry the BLO is still a natural organic material and it'll be broken down by the same micro-organisms that can break down hardwoods for example.