Some may but in general they are considered exposures to risk and will be excluded or your coverage may even be canceled. You will need to speak with an agent or agencies in order to find a company that will accept a trampoline risk.
Of course they can. It's part of the insurance contract. You also have the right to refuse the inspection; this would likely result in rejection of your application or a refusal to renew coverage....
There are many insurance companies that offer homeowners insurance and it will vary from state to state. I recommend that you call an Independent Insurance Agency. These type of insurance agencies...
Not all companies do, it is a specialty of some insurance companies though. Your best bet would be to call an independent insurance agent that can find the specific coverages that you need.
Most customer reviews dictate that Kwik home insurance is an average insurance company with most of the complaints centered around their customer service.