If you only have that time, I would rebook to fly in/out of Ayers Rock. You could try booking into Alice and out of Ayers, but you will be cramming alot into a very short time.
Definitely make reservations - rooms are limited, and if they're full there isn't much you can do about it. I bough non-refundable airline tickets for my parents & I before checking on room availability and got shut out. After a few days of trying for cancellations, I got lucky... the YHA, four to a room, bunkbeds, shared bathroom down the hall. For a week I called almost every two hours to check on cancellations, and right before our plane took off, I managed to score the most expensive rooms in the place. As I couldn't face putting my parents into a youth hostel, I had to pay up.
We went in September... the days were warm (around 30) but the nights were about half that. We had rain one night too, which they told us was unusual.
WRT tours - the hotels will have some on offer. We did the Sunrise Tour and a walking tour around the base. Both were great and we arranged them upon arrival.
Btw - I would recommend the "Sounds of Silence" dinner as well... again, I'd book before arriving...