When I spread my hand from thumb to tip of my little finger is about 20cm (near enough, I'm over on that, and under on the arm span, but we're estimating here and I know how much extra, so I just put my thumb a little inside where my pinky was the previous time)
For height, it's really just a matter of training. You're accustomed to thinking about it in feet, so you can judge more accurately in feet. You're probably just as inaccurate in the inches as I am in the cm (or maybe I'm off by 1 more... who knows) when estimating. That's why they're estimates, not measurements. I bet I'm pretty good at estimating heigh in meters though! (That person over there is about 2m... and person unless they're a child, in which case they're about 1m!)
For games, it's kind of arbitrary anyhow, but so far as I can tell, even USA track meets are done in m.
American football is the only game I can think of that uses Yards, but I admit I have no idea how big a basketball court is, nor how far between baseball plates. Fortunately google knows.
Court is 15m wide by 28m long, in the USA it's 50ft x 94ft.
Baseball plates are 90', but bizarrely there's apparently no standard for where the home run fence is (I guess that's some Imperial uncertainty)