Our Explorers aren't smart enough to throw many codes for the transmission (I think only the guys that do an auto to manual swap get codes since the whole harness is disconnected). You certainly won't get codes for lack of fluid or pressure. If you run out of fluid for any reason, the transmission will just simply fail to engage. You'll be sitting in drive with a high idle and not moving anywhere. That's all.
Yes, that's your transmission pan. Fairly easy to get at to replace the internal filter. Just leave a couple of bolts in place and then break the seal on the pan and be prepared for a bath of ATF. I was super careful but ended up getting it all over my shirt & arms.
I'm impressed that you got an Explorer up to 100 miles an hour.
If yours is a 4x4, your system probably holds beyond 8 quarts. All told, when I did mine, I think I put 5-7 quarts back in before the transmission would engage again. I added the recommended 3 or 4 quarts and it did absolutely nothing. If I were you, I'd buy 5 quarts and start there.
Also, do you have a gasket for the pan? Don't use those cork & rubber mix gaskets. I put one on mine and torqued it to spec, painfully alternating and doing incremental torques. Looking at it now, it's leaking again and all squished out. Piece of junk. If I wasn't dropping the pan again to change a seal, I'd be super pissed.
Definitely check out that check engine light. It's easy enough to pull codes and there's plenty of online databases to tell you what's going on. Like I said, these vehicles aren't super smart so most check engine codes are relatively easy to fix.