It might.

Lots of citations never get reported to insurance companies, and insurance companies don't check records constantly. Some companies also ignore certain violations if there are not multiple violations.

Nothing you can do about it now. Sit tight, keep quiet about it and see what happens.

I think I'm seeing a familiar pattern with this. You plan to just keep asking the same question over and over until someone tells you what you want to hear, then you plan to insist their answer is the correct one.

If you really think that's how it works in the real world, keep posting your question.

It can take two Months.
They DO NOT CARE you are having a Birthday.

You are required to Produce a VALID License when requested by Police. So if you are a good driver you should not needing to Pull it out that often.
Need it to buy a Drink. You will survive waiting a few days to celebrate the big day.

There is no way a parked vehicle can be deemed at fault for an accident. Well sometimes there is, but you'd have to be parked a whole lot more badly than what you're thinking. I'm talking parked on an airport runway, across a train crossing, or in the through lanes of a freeway. Anything else, even if you were parked over those little yellow lines, and it's 100% the moving vehicle's fault.

You've probably heard that myth that all parking lot accidents are split-fault decisions, and it is a myth. While there are a lot of 50-50, they all happen when both vehicles are leaving from parked positions, they back into each other, and each driver insists they were there first. But when one vehicle is parked and the other is moving, there is never any dispute about fault.

Your pick of best answer, just so you know, is completely wrong. Well intentioned for sure, but still wrong.

For you to be responsible for a rolling shopping cart striking the other guy's vehicle, one of two things would need to happen. Either you freely accept responsibility for the damage on record, or the other guy has to convince a court of law that you knew (or should have known) that the shopping cart you hit would then hit his vehicle. And that second thing isn't going to happen. No judge in the world would believe that you're good enough and evil enough to pull that off, not even if the other guy hires Johnnie Cochran as his lawyer.

When a shopping cart strikes a vehicle, it's covered as a Collision claim. Insurance companies don't look for whoever pushed the shopping cart last, because it doesn't matter. Shopping carts roll into vehicles all the time, multiple times per day in any town, and it's one of those things that just happens.

Tell the other guy to go ahead and report it to his insurance company. He'll get madder than the devil when he finds out only his Collision coverage will fix the damage, he'll get even madder when he finds out it's subject to his deductible, and then he'll really get mad when his insurer tells him they're not suing anybody to recover the money. Because insurance companies don't file lawsuits when they know they can't win.

The problems that are causing high insurance rates for you are:
18 years old
(presumably) male
Single
Living in Los Angeles.
Audi

Unless you can change some of the above, and since you have sought 3 quotes, I see no solution.

It is $6,000.00 not 6000$