I am interested in recording and live streaming the game as it stands now but I don't see any notice of if there is an NDA?
You are free to record and stream the Alpha release right now. People have been doing it for awhile now. :)
Yep, go for it!
YouTube asks for some official statement from the game devs saying "it is OK to record Let's Play videos" or something similar.
An example for Minecraft is like this:
It would be nice if something similar was for Eco