Growing up in post-Apartheid South Africa history is sometimes a very difficult subject, especially the Great Trek. It became very politicized and to some extent romanticized during the Apartheid era as the government tried to them as the founding fathers of the country.
Part of the rhetoric used was that Shaka Zulu and his wars shortly before depopulated the area by either killing everyone in his way or forcing them to move North into what is now Zimbabwe. The trekkers therefore moved into unused and empty lands and did not steal it from the locals.
How truthful is such a claim?
Another claim is that where there were still people the trekkers bought the land legitimately and was double crossed and attacked by the same people they had arrangements with after they settled.
All of these is in some way to redirect the source of the conflict between black and white away from the whites in some way and lay the blame on the other party.
This question, particularly the question of the Empty Land Myth and the Mfecane has been asked here before. /u/khosikulu has provided several excellent answers, including here and here.
The take-home message is that the Empty Land Myth is a myth. The military revolution coupled with expansion of trade linkages in the first decades of the 1800s resulted in much conflict, and a lot of reorganization of political-social networks, but there absolutely were still people living in the area when the Trekboers arrived.
For the second claim you mention, I don't recall any prior discussion of treaties in this subreddit. Also, I am not well informed enough on South African history to really address it. I expect that if Khosikulu sees this thread, he could provide greater insight.