While I do not work for Farmers, it has been my experience that they do allow exclusions. Usually, you will need to call your agent or a customer service representation at their call sent and request an exclusion form.
Although I am not a Farmers insurance agent, my understanding of Farmer's Roadside Assistance program is you can either call their roadside service while your vehicle is inoperable and they will tow you up to $150 or you can be reimbursed for your troubles. However, this is all dependent on having towing and roadside on your policy.
While it can vary by company, insurance will follow the car rather than the driver. So, in the event you get into an accident in your dad's vehicle, his insurance would be primary and yours would be secondary.
Typically, car insurance follows the vehicle (not the driver) so if you were to file a claim, it would be under your friend's insurance. However, I would exercise caution when considering filing claim.
Because California uses mileage as one of their biggest rating factors, she should be able to find insurance that can accommodate her needs. However, she would need to show proof of how much she drives.
In my opinion, you would not benefit from filing a claim since the repair costs are so close to your deductible. Our State of Auto Insurance (page 58) report shows that an at-fault accident in California has an average impact of $899 per year in additional premium.
Roadside assistance varies by insurance company. From my understanding, most towing and roadside assistance coverage offered as part of an auto policy either has a set dollar amount to cover a tow, covers towing up to 15 miles from your breakdown, or covers towing to the nearest repair facility.