Haven't been through there for around 12\14yrs.
But West Mcdonnell ranges is a must.

Others will give more modern info.

Waeco.

My original 50ltr. I had 3 x 85w and 1 x 50w panels on van with 2 x NZ70Z wet cell battery's to run van.
also a 12v outlet plug in side of van,
where table sat. to plug in fridge if using outside.

Usually though.
The Waeco sat in back of Patrol where seat behind driver was removed.
second battery under bonnet..
With an 80w panel, mobile.

Moving regularly.
that was self sufficient,
But the 12v outlet from van came in handy on inclement days.
ALONG WITH the GENNY I always carry.

Air cond. tools etc.

If no air cond, a 1kva will cover you.
Just have a 25\45a Mains 4 way charger
for bulk charging.
Genny 12v outlets leave a LOT to be desired.

No matter how much solar you carry.
No SUN. NO power. simple.

have backup. a little $350 Chinese genny will cover most.

And have fun. Not all days are bad.
when first starting out. double check EVERYTHING before moving.

I've been vanning for over 50 yrs. Still make mistakes.
Specially when on first coupla days of fresh trip.

Go round and check everything b4 starting engine. and have missus go round rig too.
In OPPOSITE direction.
Women normally have sharper eyes than men
(from finding things to nag about chuckle)
She'll often see things you forgot.

Usually I do outside of van.
On arrival and dep.
Madam sorts inside. stop and start and during too.
Less any heavy lifting she needs.
That goes for at home too.

Enjoy.
It's a great life. and gets better as you go along.
As long as you can free yourself of the housebound fetters.

September 2016 we stayed at Heritage Caravan Park in Alice Springs, reasonably priced and amenities were OK.
It's well worth staying in the caravan park at Yulara, not cheap, but everything is there

The only place you can stay reasonably close to Uluru is the caravan park/resort at Yulara. There are cheaper places like out at Curtin Springs Roadhouse, but what you save you would use up in travel cost and time going back and forth!
How long depends on what you like doing. We have had more than one visit there, just because we like it. But we like walking, so have done the walk right round Uluru - that occupied a goodly part of a day. Another day we walked it again - the other way - because it looks different that way! Is also a long walk at the Olgas - the Valley of the Winds walk.
Definitely 3 or 4 nights there.
Have you thought about going up to Kings Canyon? You would need to backtrack somewhat to stay on sealed roads, but if you like walking is well worth the effort to get there.
Alice Springs has quite a bit to do around the town - to do with history, culture, environment. Do not miss the Desert Park. You will need to decide if you are going to use Alice as a base and do day trips out into the Western and Eastern Macs, or if you are going to also take your van out to somewhere like Glen Helen.
Can easily occupy a week there.
We most like the MacDonnell Ranges Big 4 Tourist Park - south of the Gap, quieter, secure.
Another interesting place to go see in those parts is Gemtree - about 120kms to north, on Plenty Highway. Different. Can try zircon fossicking with them. Very scenic area.