A few thoughts:
As for that football shot and whether or not you had anything to do with it, being in the right place, at the right time with the camera on the right settings is what it's all about, so don't sell yourself short.
As a for instance, this football shot always stood out to me after I took it. I love the reactions in the background, the guy on the ground ... all that stuff. I was standing behind the endzone when I took it, which is rare for me. Usually I'm at least close to the line of scrimmage, a few yards ahead or behind. That usually offers the best chance for a good photo, and it's much easier to take notes on the game from there. But this time I was talking to the car to get a different lens between quarters, and this guy broke away on the last play. Thankfully, I was ready to roll and could easily take a knee and pop away. I've tried to get stuff like this at other games, but geez, I just can't sit in the endzone the whole game like the full-time photogs can, and it simply never works as well as this one did. You have to take some risks to get standout photos sometimes, and you have to be ready to take advantage of what chances to do get. You were ready with that football photo, and that's not dumb luck.
As for the gymnastics photo, hey, again, you can't always been in the absolute best spot, and for a spur of the moment thing, that's a good shot.
Very generally speaking, though, the lower your angle on something like that, the better the shot. (If I'd been squatting a little more, or on a knee, for that football shot, you'd be able to see the kid's face better.) I love getting way low for wrestling photos. I don't have one of those little view finders that prevent you from having to flop on your belly, but that'd be wonderful. I don't do it all the time. A lot of the time there isn't room, and I'm only willing to look like a strange guy sprawled out on the ground for so many minutes a day. BUT, it does typically make for better photos of something like that.
Finally, I don't understand the debate about cutting limbs off. I don't think that's a horrible thing to do, and do it frequently myself. It can definitely be done awkwardly, but it doesn't have to be. I sometimes have to remind myself that a great shot doesn't have to include all the body parts or everything I captured in my frame to tell the story. Like in that basketball photo above, if the girl's scrunched up angry face is the story, crop whatever you have to crop to make sure that's what draws reads' attention. People will fill in that she has arms and legs by themselves.
Here is an example I just worked last week. I had this kid's whole ski, and the entirety of the other kid, too, but it was going to take a fairly awkward crop to include all that. My story was about the kid we see the most of, and I think what I did crop out -- part of the ski and the other kid's body -- still allows the story to be told. This isn't a great photo. If I'd been stationed a little differently I could have had both bodies with a lot less empty air between them. But, I use it just as an example for this discussion:
