There's no way the oil filter was factory. That thing would be clogged up after 10k. And I don't know what kind you got but the Motorcraft FL-820S is the best choice for these engines. They have the anti-drain-back valve to keep oil in the top half of the engine so it's not dry on a cold start. It's also one of the cheapest. I use Motorcraft 5W-20 or 5W-30, whatever is available - Walmart has 5.25 quart jugs for $11-12.
Regarding the transmission, Mustangs use the same transmission. Their valve bodies might be slightly different for firmer shifts, but if that's the case, the J-mod will give you even firmer shifts on your original valve body. They also have a different tune for higher RPM shifts in their PCM. Only way to change that is to get a custom tune to install on your PCM which will run you a few hundred bucks. The J-mod will be less work and cheaper than getting a different transmission with a better outcome as long as the transmission is still in a reasonable condition (clutches aren't worn out, and yours don't seem to be). You just have to buy one or two drill bits, snap-ring pliers, inch-pound torque wrench, two new separator plate gaskets which are at the dealer for $2/each, the filter, and 10 quarts of Mercon V;14 quarts if you drain the torque converter, too.
You can open up the rear end and flush the fluid and check around. If there's any excessive metal shavings, you might have to consider replacing parts, although these 8.8" rear ends generally run for the life of the car and then some. If anything is going to go bad in the rear end, it will be hub seals as these are known to sometimes start leaking.
If you do need to tighten up the drive train, check the U-joints for excess play. If you want to upgrade to a higher gear from the stock 2.73s, you can usually find 3.27s off of junkyard police interceptors. 3.55, 3.73, and 4.10s are also available for the Ford 8.8". You can also get a Trac-Loc if you wanted a limited slip diff. I'm saving up for the trac-loc as my next modification and possibly 3.27s.