I stayed in a tent cabin most recently in 2010. Loved it! But it is a little rough. I would be surprised if any of this has changed, but you might want to confirm with the concessionaire.
1. No. You can park close to your cabin to load & unload, but then you need to move your car to the lot. No big deal, it's not far at all. ***BTW, take anything with any scent out of your car! Bears will think it's food.
2. There are no fire rings, but we did see others cooking on camp stoves at the picnic tables (each cabin has a picnic table & benches). Wish we'd brought ours!
3. Not sure what you mean by "entertain". What do your kids like to do? There are ranger programs at the amphitheatre near the campgound across the road - maybe a 5min drive or 10-15min walk - and those are very kid friendly. (Check the schedule.) There's a small visitors center (the one in Lodgepole and the museum at Giant Forest are bigger); if they're doing the Junior Ranger program, they can get their books stamped etc. There are some trails nearby (e.g. Panorama Point), and of course Grant Grove is only about 5min drive or 10-15min walk. It's a nice peaceful area to just walk around in the morning and evening.
4. No camp fires at the cabins.
5. Absolutely! You'll use it somewhere. Also more sunscreen than you might think. I also spray down the cabin before unpacking (some might consider that extreme, though). Consider a citronella candle or similar if you're going to sit outside.
6. Don't know, but I don't think I would risk it. Those cabins are tinder boxes. Do bring extra lamp-style flashlights - the one they'll give you doesn't provide nearly enough room light.
7. Oh yes! Broom; Lysol; doormat; folding chairs for outside (lots of stars to enjoy!); your own breakfast & lunch supplies, as park food is meh, and dinner supplies if you have a camp stove; buy the hiking trail maps sold at the visitor center/gift store; shower shoes; bath towel, so you can use theirs for a mat while changing. Extra lamps and flashlights as noted above. Games or something for the evening. Change for the payphone if you need to call home (no cell signal). Something to cover any coolers you leave in the cabin while you're out.
8. Food is priced as at any tourist area in the middle of nowhere. The quality is pretty low, though - read the reviews. Menu (dinner - I haven't had bkfst or lunch) is a mix of standard diner fare (burgers, basic steak) and more ambitious items (chicken piccata w/ saffron rice, some eggplant thing), but none of it really hits the mark. A burger was the best thing I had. Service was mostly bad - friendly, but bad. ***The little pizza place attached to it is pretty good, though. It uses the same kitchen, so go figure! The tv is usually set to some...game...somewhere.
That said, they're probably new employees each year, so you might strike gold!
There's a coffee cart outside the gift shop, or you can go around the corner to the market. The market also has microwaves for any food you purchase there. And a decent selection of ice cream treats. :-)
The restaurant at Wuksachi Lodge (Lodgepole area) is apparently better, and a lot pricier. There are fast food lunch counters at Lodgepole and Cedar Grove, and a reservations-required restaurant at Stoney Creek. Montecito Sequoia used to have a public restaurant, but I don't know if that's still the case.
9. Sorry, don't remember but I don't think so. Also, I've heard conflicting reports about whether or not they're charging extra for showers now (they didn't used to); I would contact them about that.
10. Yes. Also, there are electrical outlets in the bathrooms.
Sorry, I don't have any pics to share. The photos on TA are pretty accurate, though. Mostly they're of the rustic or camp cabins, but the interiors are pretty similar.