As if you can't tell by my posts already, I'm a woodworker with well over 30 years experience.
TheEngineer is correct, if you dont do something with some kind of finish it will turn grey over time.
You are only prolonging the natural look, it will turn grey eventually anyway from the sun.
No, the post are just set 3' deep and are about 6' above the ground.
Just make sure you tamp the dirt as you fill in around the post.
The top rail is a half lap joint on top of the posts, then lag bolted on.
Yes, that swing does have a marine gloss finish on it, no stain and it is Cedar.
If you like the natural look, clear coat them with an exterior marine polyurethane.
I just made 2 swings for our lake property, they aren't as long as the one you made, mine are about 50".
My swings also are mounted on just 4x4 post in the ground with a 4x4 cross piece for the swings to hang...