Lasseter is Uluru and Kata Tjuta country, in the red centre about 440 km south-west of Alice Springs. Uluru rises 348 metres from the plain, Kata Tjuta is a group of 36 rock domes, and the park is run jointly by Parks Australia and the Anangu traditional owners, who have lived here for more than 10,000 years. Climbing Uluru has been banned since October 2019.
There is no camping inside Uluru-Kata Tjuta National Park, so for Uluru you stay in Yulara, the resort town about 18 km from the rock, where the Ayers Rock Campground has powered and unpowered sections. If you are also going to Kings Canyon, Kings Canyon Resort and Kings Creek Station both have powered sites, and along the Lasseter Highway, Curtin Springs is a rest stop.
The Uluru Base Walk circles the rock at ground level and suits a range of fitness levels, and the shorter Mala and Kuniya walks take in rock art and Anangu stories. The park has 73 reptile species, so keep an eye out for lizards on the paths. On the drive in, the Emu zoo is next to Desert Oaks.
At Kata Tjuta, the Valley of the Winds walk is steep and rocky in places, with two lookouts, and closes in extreme heat. Around Uluru there are lookouts, including a sunrise lookout.
Summer days here can pass 45°C, with UV readings of 11 to 15, so walk early and carry plenty of water, and pack warm clothes for winter nights that can drop to around -5°C.
Yes. 3 campgrounds here have powered sites confirmed: Ayers Rock Campground - Unpowered Section, Kings Creek Station and Kings Canyon Resort. For the rest we are still confirming, so check with the park or holiday park before you book a powered site.
Uluru is about 440 km south-west of Alice Springs by road, roughly a five-hour drive, and Yulara is 428 km. You can also fly into Ayers Rock Airport, about 6 km north of Yulara, which has flights to Sydney, Melbourne and Cairns.
Facts from Wikipedia, "Uluru-Kata Tjuta National Park" (CC BY-SA 4.0) and Wikipedia, "Yulara" (CC BY-SA 4.0).

Region boundary: ABS ASGS Edition 3 Tourism Regions 2021 (Tourism Research Australia), CC BY 4.0.