I'm no lawyer, so this advice is worth what you paid for it.
1. The police can investigate complaints. I'd bet they can make a pretty good case for why they needed to step onto your lot and ask you questions. I doubt there is anything you can do about that.
2. If the police are issuing a summons, I wouldn't mess with them unless you want a summons for interfering with a police officer.
3. No. You don't have to permit the police to enter your place of business and they aren't permitted to simply go wherever they want. But you have to tell them that and you'll have to suffer the consequences of those actions if you do. I doubt they can make good on their threat to tow every car on the lot but they can make a LOT of trouble for you. For example, they can decide to do "special" enforcement and issue citations for all cars with irregularities, run all the license plates checking for outstanding warrants, etc.
The police also are often friends with local regulators who may want to stop by and ensure that you are complying with all local and federal laws, etc.
4. No. It's not okay for the police to single you out and harass you. However, you'll have to provide some kind of proof that they are doing so intentionally and that's pretty hard, especially when there is a history of noise complaints at your business.
It seems to me that unless something egregious happens, you are stuck with this situation.