Q. who/what exactly were those strange olive drab elf she-folk thingys under the Red Tree?

The tricksy hobbitses are the Children of the Forest. They are the sort of magical beings that lived in Westros before man.

What happened to the Red Tree? Does that matter pro/con? (did the Starks not have a similar tree thingy on their lands?)

Dunno about this specific tree, but there are Weirwood trees all over the place. Mostly in the North. Yes, there is one in Winterfell. It's where those that pray to the Old Gods do so, and what act as the "eyes" for peeps like the 3ER and Bran whe they're doing their magic seeing thing.

When men first came over from Essos, they warred with the Children of the Forest, Giants, and other previous inhabitants of Westros. They cut downlots of Weirwoods.

"Bran and the Three-Eyed Raven enter a vision to transfer the Three-Eyed Raven's knowledge to Bran."

Okay, so what abilities does Bran now have per the transference of Tree think?

No one knows exactly. Basically he's the 3ER now but doesn't really know it.