Finally, you can't shave *that* much weight off the car even if you stopped worrying about crashworthiness altogether; you can only make a steel box for 4/5 people so light, and still make it ride nicely, not be noisy inside, have comfortable seats, be able to fit people over 6' tall, etc.
As a first step you could roll back vehicle weights to what they were 40 years ago. You can also shift from steel to lighter materials, and you can eliminate the entire engine compartment (using small hub motors instead) so you can simply chop away much of the existing vehicle. Further, in an autonomous-vehicle world, it seems very likely that individual vehicle ownership will largely become a thing of the past, so you wouldn't have to have a box for 4/5 people except on the occasions you actually have to transport 4/5 people. Of course, the smaller you make the vehicle the less surface you have for solar panels, unless you have something like a highly-streamlined "solar umbrella" which is larger than the vehicle.
As for solar panels, again, no, it's completely impossible. At highway speeds, you need tens of horsepower to overcome air resistance.
Depends on streamlining, and on what "useful speed" means (you said highway speed, not me -- the solar challenge vehicles go much faster than bicycles but not highway speeds), and on how much you can rely on batteries. I know I said "from on-board solar panels" but didn't mean to preclude the idea that the vehicle also has batteries. If the vehicle is parked in sunlight a significant portion of each day to charge the batteries, and it's very light and has very low air and rolling resistance... it may be possible that it can operate usefully without charging from an external source. Or perhaps just without very much external charging.
Also, you're implicitly assuming that the vehicle must overcome air resistance by itself. That needn't be true with autonomous vehicles at highway speeds, which could close up into big trains drafting off of one another. Perhaps the vehicles in the train could even join electrically or physically, so that the lead and trail vehicles don't have to draw down their batteries to maintain speed.
There are options, and I don't think the possibility should be dismissed out of hand. It's a stretch, certainly.