While in this area I think it is worth a detour to Kings Canyon (warning - it will be very HOT on the floor of the canyon this time of year).
However, when I visited a few years back the through road to Alice Springs from Kings Canyon has sand (quite deep in places). So unless you have a good 4WD you need to backtrack to the main road. Since its quite isolated in parts on this route, check you have emergency equipment including a radio (get shown how to use if you dont know), plenty of water, etc.
And of course Kata Tjuta (the Olgas) are also a must - just 15 or so km down the road from Uluru.
I dont remember too many gas stations between Alice Springs and Uluru (maybe a couple?) so keep gassed up.
All the accomm at Uluru is IMHO overpriced for what you get. However you wouldnt find me camping - with the snakes, heat, cold!! (night is surprisingly cold - we had frosts in early April), dingoes

etc.
Unable to help with the rental car questions.
Edited to add: You're spending just a week on the other side of the world and taking 3 days travelling to and in the interior!
I dont think I'd find it fun doing that much driving in the circumstances. Can you fly into AYQ (Uluru) instead of ASP (Alice Springs)?
Another thought if you are driving - watch out for kangaroos on the road in twilight and after dark. You dont want to hit one at speed - they are reasonable size and so will do a lot of damage.
[This message has been edited by Kiwi Flyer (edited Jan 17, 2004).]