If the tow company acted on its own for the fire lane violation then the first on your list is out. This is what I had initially thought was the situation, that a representative of the property had requested the tow.
They apparently did provide you a copy of the towing authorization- it listed the fire lane violation. It is posted above. The second on your list is out.
Tow signs usually have a phone number on them for local law enforcement, but the sign you provided is a no parking sign, not a tow zone sign. Are there other signs in the area that indicate the tow company and contact info? Did the tow company mail you a notice after the tow? If not, then there may be an issue to address appropriate signage and notice. As I mentioned before there may be an issue with the sign shown as it may list an outdated fire code that no longer exists. If so, the fire lane might not be legal.
I believe you do have a valid complaint about the photo for two reasons. First, the photo was supposed to be provided to you before payment. Second, you indicated the photo you later received was edited and it may not clearly show a violation that justifies the removal.
I don't believe you indicated that you ever checked with law enforcement when attempting to find your vehicle. How do you know they did not report it? I bet they did. You can call and provide your license plate to find out if there is any tow record.
If the tow company has prior authorization from law enforcement they may take the car more than 10 miles. I would expect most companies in the LA area have this authorization.
Most of what you provided in that last post is of no use to you. If you want to make a complaint to the district attorney about the tow company they might look in to those possible violations.
Your focus should be on the legitimacy of the fire lane, the failure to provide clear photographic evidence prior to payment, the apparent failure to provide a copy of the tow agreement with your rental property, and perhaps failure to give notice/inadequate signage (there may be a single sign at the entrance if the property naming the tow company and giving contact info).
Your damages are the fees you paid for what you believe was an improper tow, which the court could award up to 4x. Forget that they may not have followed procedure- you're main argument is that you were not in the fire lane to begin with. If it is determined that you were in the fire lane then you have the other issues to resolve.
No, you won't get to pile on more damages for multiple violations, but if the tow company is investigated it could be fined for each violation.