Hey Nick,
Welcome to the Forum!
Ok, so I'm going to take this out of order...
1. Yes, get those transmission updates. The majority of transmission issues can be traced to missing a software update. If the shifting is still bad afterwards, have them reset your transmission to factory detail values (called the "adaptive values").
2. Now, yes, the rear differential (called the Rear Drive Module or "RDM" on the Cherokee), often leaks on the driver's side. It's due to the shaft inside the RDM being substantially shorter (about 6 inches) than the one on the right side (which is about 24 inches). As a result, you'll notice a lot of up & down play on the driver's side that's not present on the passenger side. That's actually normal. The seal on the drivers side wears quicker and needs to be replaced as you'll weep oil from it. Note, that while the corrective action is replacing the seal, if funds are tight, another valid option is just adding more gear oil (70W-80) to the two fill plugs on the rearward-facing side of the RDM. Will you have the weep still? Yes, but as long as you periodically add additional gear oil for that which is lost, there's no negative result.
To add oil, you need a 3/8" ratchet. Your Trailhawk as 2 fill plugs as shown in the photo below with the "1" and "2". Fill both to the bottom lip of the fill hole using Mopar 70W-80 gear oil.
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3. Here's what the weep looks like. Yours is probably the same. Many of us have it.
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New seal (left), old seal (right). Seal (Part below). Dealer or any mechanic can replace it.
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This is your Left-rear halfshaft (yellow) and note, there's only a 6" stub shaft that enters into the RDM (red). Because of the shortness, it only goes through one set of bearings hence even when fine, there's substantial up & down play. This is normal. If you do a Search in this Forum, you'll actually find members who have posted
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Here's a video of
abnormal shaft wobble. Again, on a Cherokee, there will be some wobble though.
https://www.jeepcherokeeclub.com/th...y-output-shaft.252063/?post_id=3068092&nested_view=1&sortby=oldest#post-3068092
Here's another one that's a bit much play:
https://www.jeepcherokeeclub.com/posts/3044549/
4. Regarding the top leak leak, there's a black top plate and then under that a blue seal that seals a hydraulic fluid reservoir the RDM uses to engage its internal clutch for the 4WD to work. Now, the only real thing that can leak there is probably if the black top cover rusts through, it could happen. However, one thing I noticed in your photo is there's fluid around the small vent tube extension. (see red circled area in the photo below). I wonder if your rubber vent hose has backed-off or isn't tight and fluid came out the junction where the rubber hose is on the nipple (vent tube extension). You'd need to make that call - just for good measure, possibly see if that can be pushed on further. Either way, if the fluid does get too low one day then what will happen is you'll get a message on your instrument cluster that says "SVC 4WD". If the fluid gets too low the RDM won't be able to build enough pressure to engage the 4WD. So, one option is to live with it now (knowing one day the fluid may need to be topped-off and probably, the top plate replaced) or do it now.
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Hope some of this helps...