Most insurance companies do have access to a driver's background when they quote and insure them. Not having a driver's license is usually an issue for insurers but it's not impossible to find insurance for an unlicensed driver, and that seems to be the case in this situation.
I do not know any insurer that offers a temporary suspension of insurance coverage. You could lower all coverages to the state minimum to make it cheaper, but if it is going to be more than a few months you may want to consider suspending the tags and discontinuing insurance.
Unfortunately, it's not that simple and there are many reasons to file a claim not necessarily as a result of reckless driving or other risky driving habits. Insurance companies do not look at the reason for the accident, they look at whose company paid the claim and what it cost them.
Most companies will allow you to get insurance again even if you have canceled a policy with them in the past. Keep in mind that having continuous insurance coverage gives you a better rate so the price will likely be higher when you restart your insurance policy, and certain companies won't insure you if you have a lapse in coverage.
If you're determined at-fault in the accident, you are responsible for the other driver's damages regardless of whether or not they're insured. You might be thinking of no-fault insurance, which Pennsylvania has voluntary participation in.
You only have to pay a deductible when your collision or comprehensive coverage pays for damages to your vehicle after filing a claim, so no, you will not need to pay a deductible in this case. I also recommend reading this article regarding claims to see how this will impact your rate.