I use
San Xavier Insurance along with a number of friends and yes you can get it online. Should be able to get estimates online from all companies. Don't bother going by what the car is worth to you ... simply Blue Book.
Most gringos don't have problems so there are seldom horror stories ... or any stories of the actual service. The few I've heard depend totally on the situation. The horror stories usually involve commercial vehicles because the companies have their insurance issues down to a science