They are currently reusing the first stage which is sub orbital - ie. Much slower, less re-entry forces. Still a major economic benefit for overall rocket cost. That said, Starship is planned to land from orbit & be reusable - let's see.

NASA is all over it from what I see - SpaceX has essentially captured virtually all of the commercial launch market and a good chunk of defence and science markets except for hyper specialized requirements or non-US defence launches.

I however don't see how NASA could have developed it given the politics involved with its funding essentially incentives Project thinking over Product thinking - I actually use that as an example when I contrast Project vs Product at work. SpaceX had to blow a couple of dozen rockets AFAIK to get to a stage where they land reliably - doubt NASA could have justified that to the US Congress. NASA's funding incentives encourage a risk averse approach to engineering ever since the very high profile failures in space shuttle and the early Mars missions. Witness how the Mars helicopter was rated for a low single digit of missions and has now completed a few dozens.