I haven't completed the whole trail, but I've done several sections. If you have the time and plenty of experience navigating in rough off track conditions, doing a side trip (adds 1-2 days depending on how fit/fast you are) up Mt Giles is well worth it. I did it a few years ago, the Rangers can probably still give you a contour map (100m contours), that has a couple of springs marked on it at the bast of Mt Giles...there wasn't a huge deal more mapping available back then (2004). The view from Mt Giles is probably the best view I've had in all of Australia. I hope to go back there in the next couple of years and sleep on the top (that will be rather cold in the winter).
Tents...it very rarely rains in this part of the world, particularly in winter. You can easily get away with sleeping under the stars every night, though I would carry a light tarp (~8x10) just in case. I would only carry a couple of pegs, if it looks like rain, you can find a sheltered spot from the wind and use sticks for poles and rocks/natural anchors for pegging it out without hassle.
Cooking...rules on fires may have changed but check with the rangers, it was no problem back then for us to cook on fires. In many of the campgrounds there are fire places, and elsewhere fire is such a big part of the ecology of this region that having a small open fire to cook on is no big deal at all, as long as you don't set the place alight or use wood that animals might use, etc. A little bit of spinifex is an excellent fire starter. A bushbuddy would definitely be fine to use if you have one.
Footwear...like Roger said, this region is HARSH underfoot. Some areas the rock just rips rubber soles apart. If you use trail runners, start with a new pair. I'd take a small unopened tube of superglue. Don't be surprised if after ~250km your shoes are knackered. I'd definitely recommend a good pair of gaiters (canvas ones are better than nylon in my experience, avoid goretex, it will just be perforated goretex by the end) or some tough pants for spinifex, particularly if you are going off-track. Normal nylon travel pants (eg like Columbias) don't provide much protection against spinifex, it often pokes straight through.
Temperatures...in July its pretty common for it to get to zero or below every night. During the day it can sometimes only get up to say 14 or 15C too, or it could get up to the high twenties. It is the best time of year to go there though for sure.
Food drops shouldn't be an issue to do, unless you have a burning desire to do it "unsupported" then I would use one or two. Several tour companies now will take walkers to/from Alice Springs and will be able to provide info on the best place for food drops and arrange that for you.
Definitely build up the trips before you go and do one of a few days. You are from Adelaide? Head up into the Flinders to get a bit of a taste of what the terrain is like if you can, and head off track if you can. If you want to get experience fast its good to learn from other people (though hard to find UL bushwalkers in Adelaide!). The Adelaide Bushwalking Group often have trips into the Flinders. Someone there will probably have a good trip planned for the Easter LWE that you could attend. I don't know anyone from the club but you can look them up. AUMC (Adelaide Uni Mountain Club) also do trips up to the Flinders most long weekends during bushwalking season; I can put you in touch with some of them if you like, I think you can join these days even if you aren't a student.
Had a look at your gear list quickly...Your Osprey packs will handle food and water loads no worries.
Good luck, you guys will definitely love this trip!