The information on Limpopo NP is very limited but you can contact Heloise de Villiers on firstname.lastname@example.org
for information. The existing website is being updated to provide a map and park facilities - hopefully this will be done in a month or so (things happen slowly in Africa).
Regarding your questions - you can enter the Park from KNP at Pafuri (north) or Giriyondo (south). There are chalets and camping at Aguia Pesqueira (Fish Eagle Camp - about 1 1/2 hr from Giriyondo) and Albufeira (at Massingir gate about 2 hr from Giriyondo) - A.P. has lovely views across the dam and is definately the better of the two.
You can also stay at Machampagne camp which is positioned on a lovely pool, it is a little pricey by National Park price standards but includes meals and a morning walk where they have reasonably good sightings on foot. I cant recall the website but the camp is operated by Transfrontier trails so you should find them on a web search. The same company also offers guided, self-drive 4x4 trails through the park
You can also self drive through the park (although having a guide is better experience) There are also 2 basic 4x4 unfenced camps (rustic ablution + fire place) in the park - Nnamphfule (near Mapai) and Sandalo. You can enter at Pafuri and head down the Limpopo and enter the Park proper at Mapai gate where Nanmphfule camp is located (about 150km or 4 hrs from Pafuri)....then head south for about 150km (4 hrs) to Sandalo and then another say 100km (3 hrs) to Aguia Pesqueira and another 70km (say 1 1/2hrs) to Giriyondo.....the best is to get a map from Heloise to get a perspective on location etc.
At present the Parks attraction is the wilderness and bush scenery experience and there are some new 4x4 trails being worked on. There are also plans to increase the parks wildlife viewing roads in the SW of the Park (where the varst majority of wildlife is located, partly with thanks to KNP relocation project which appears to have been a success) - this should improve the Parks tourism product to try work off the bush to beach rush reputation....a lot of work to do to get even remotely close to KNP !