How serious an offense is driving alone with an instruction permit?
In Illinois, you could be arrested for No Valid DL, a misdemeanor offense. Without a legal, licensed driver, you don't have a license.
What you described is an administrative penalty more than anything else. If you do have a permit it isn't neccesarily a criminal offense per se because what that really is is a restricted license - if anything you'd be guilty of violating your restriction which may result in fines, a temporary suspension, and insurance always looks better than not having it. As to if you would be cited or have your car impounded depends a lot I would think on why you were stopped in the first place. Maybe they would just add it to the citation and DMV could at their discretion impose further penalty. This is kind of unusual. Dosen't sound like an issue that comes up very often. If your car's insured, you might want to consider just taking the test. That's the best way to avoid it becoming a problem.
Hmm. If you were stopped for a minor offense the most common course of action is the officer will ask you to hand over the keys and probably give you the option of contacting a licensed driver to come pick up your car. This is an issue totally separate from the stop that wouldn't neccesarily be mentioned. The only way he may impound it is if he feels you were DUI and arrests you or if it is left abandoned for too long. That's because he's bound by law to not let you move it. In some cases, especially if you're from out of state it may even get overlooked. That happens often with any small restrictions written on a license. What will the state could or might do is a whole other matter. Check your licensing office to find out.
If God forbid you're involved in a major at-fault accident and it's discovered then, many officers believe it or not will actually write the ticket as if your permit is a regular license to cover your behind and keep insurance calm.
To really answer your question, it depends on the violation you're accused of to begin with, the moode the officer is in, what state you're in, driving history, etc.. it's not advisable to do this mainly because if you hit someone, your insurance can always deny a claim if they feel you're incompetent or operating a vehicle irresponsibly.
It is going to depend on the state. Look in your instruction book you got with the permit. It should tell you. Some states will revoke the permit amd make you wait some period of time before you can get another permit. Some may allow you to keep the permit but extend the time before you can take the driver's test. The most serious consequences would be if you had an accident (at fault or otherwise). Even if the accident was not your fault, there may be a presumption that you bear some fault, as you are essentially an unlicensed driver and your word won't be worth squat. Your insurance company may refuse to cover any the damages - particularly collision damage to your car. And they will very likely drop you from the policy, in which case you will have to purchase extremely expensive high risk insurance.
In Virginia, it's considered a "Learners Permit." Back when I was 15 I was pulled over for speeding (lead foot at the time) and all I had was my Learners, and no one with me. I was placed under arrest, the vehicle was impounded (the registered owner of the car (my dad) was out of town at the time) and I was taken home and dropped off by the police with a ticket/summons to appear in court. Definitely not a pleasent experience, especially when my dad came back home. So bottom line, it's the same as Driving without a license, at least in Virginia.