The truck isn't complicated.
Ford used two different types of differentials in Rangers, one was called an "open diff" and the other is a "posi-trac" (very loosely called a locking diff, although technically it ISN'T) which Ford calls TracLoc, which is what you have, positively identified by the clutch and frictions plates you have in those pictures.
The important part i'm trying to help you understand here is the difference between diffs and that one has friction and clutch plates, which is the TracLoc that you have, and the other does not. BOTH diffs will turn wheels. Period. End of story. (get the point? broken plate ears or not, even if those plates weren't there at all the truck will still move ..... and plenty more than 3 mph)
The problem you are having is almost assuredly not with the diff. Yes, it is obviously broken to **** and you should be spending the money to fix it, but it's not what's causing your truck to only drive 3 mph.
Do some research on why people call Explorers "Exploders" and you'll be taking a step in the right direction.
Sorry for your luck.