I have the idea of making a game with the design kinda Neverending nighmares, Nihilumbra or Don´t starve (like draws) but I don´t really know which game engine use and which animation program. Suggestions, please?

Any game engine that supports 2D rendering (which is pretty much a required thing for 3D anyways...) will work just fine. Don't starve was made using a custom game engine powered by lua, and I'm not sure about the other two.

As for animation programs. If you have no experience with any, than I'd suggest finding one that suits you. There is not a best, just which program makes more sense to you.

Don't starve seems to be isometric rendered so it isnt real 3D in general. You should look for an iso capable game engine. Don't starve also may use some post processing shader to get the scribbled look.

I dont know many about animation software but in that case you need something to make sprite animations