Are there houses for rent in Loreto? If so, what is the average rental cost? What is the power requirements in Loreto, 110 or 220? Is propane available in Loreto? Can you bring solar panels into Mexico?

Yes, there is houses for rent in Loreto, you need contact with a real estate agent (higher cost, but somehow could be more safe) or try your own personal search in town (rent cost more chip, and maybe you can find a good house, and a good landlord, you never know ahead).
Loreto has both kind of power, depends on the house setup, and Yes, it is propane available, and Yes you can bring your solar panels, for a personal use.