The voice actor of Lion-O's father, Larry Kenney, who voiced Lion-O in the original, let it slip that Tygra and Lion-O are brothers in this incarnation, so that's why he gets to hang out in the court. I do like your idea of the Kittens being street-cats (haha). From their clothes in the trailer that seems to be the case. As for Panthro, perhaps he's in exile for some reason. This version doesn't really look like the exploring type
I wouldn't want to see the anointment trials happen so soon. I think that would be best saved for later in the season. I do think Lion-O is going through a trial of some sort, maybe a competition with Tygra over who will succeed Claudis. And then he has to fight his father to prove his worth. It could be that the trials will happen as a seasonal arc. That would be cool.
The stones of power could possibly be like the Treasures of Thundera from season 3, but other than that I have no idea.
Re-watching the trailer, I'm pretty sure the chunk of thundrillium Grune is riding can be seen in the shot of the Cat's Lair at night, right before the shot of Grune bowing to the crowd. I don't think it's any big secret whatever it is we see him doing. My guess is that the lizard mutants we're seeing aren't quite slaves but rather prisoners of war, and Grune just got back from capturing a thundrillium mine from the mutant armies.
Lion-O, Tygra, and Cheetara all appear to be protecting lizardmen in the stockades from an angry mob. I think it's possible the three of them become wanted and are forced into the wilderness of Third Earth where they meet Panthro, with Kit and Kat tagging along with them.
Also, one more thing I noticed; there are hardly any trees or plants besides that big gnarled one in the coliseum. It looks like Thundera is a desert.
So right now here's what I think the backstory will be: It all takes place on Third Earth, and Thundera's a kingdom, like Will mentioned. Races of cat people, lizard people, and other Half-Human Hybrids
have evolved. At some point Mumm-Ra awoke and tried to take over with a mutant army, but was beaten by Claudis or some other past Lord of the Thundercats, and now after many years he's returning.
Another theory I have is that perhaps Mumm-Ra or the Ancient Spirits of Evil had some hand in the creation of the mutants. In the old show two of the spirits were a crocodile and a vulture statue, which could have fit for Slith and Vultureman. If there had been statues for a baboon and a jackal (instead of a bull and boar), I would have been totally convinced.