Customers can send technical support or other requests to project owners, it is ok. But in this scenario, I want to create and assign requests to the customer. For example, I notice a bug in my customer's system and I want to warn them. How can we do this, without commenting customer's open or closed issues?
You can only "assign" an issue to an Agent. So if you want one of your customers to be assigned an issue you must make them an Agent which consumes a license. I do not advise this as it gives them full access to the project which generally isn't wise. The best thing to do is open an issue on their behalf, i.e. set them as report and simply transition to "waiting for customer" w/ appropriate messaging.