1 - SHOULD I refrigerate a carbonated keg? Why?
2 - What taste changes does the beer go through during the aging/conditioning process that would cause me to want to keep it in the keg and age a few weeks/months? I know the short answer is to try to age one and give it a try but my palate is not that good and if its not that worth it then I'll just keep doing things the way I'm doing it.
I wish I could remember where I originally heard/read this, but as a general rule, refrigeration is a precursor to serving. Leaving a bottle or keg in a (mostly) temperature-stable (and light-free for bottles) room is what I'd consider standard practice for "cellaring" a beer. How long it can sit is dependent on the beer style--a good Hefe isn't known for its age, while a fine Barleywine has likely been sitting for at least 6 months to a year. As it relates to homebrewing, unless the beer is filtered, cellaring allows most things still suspended to settle out naturally and contribute to the flavor. Refrigeration will shock yeast into settling out quickly and by extension, the cold will generally force other particulates to drop out as well. I'm not patient enough to do an A/B/X to find out how flavor would be impacted.
This is strictly my opinion, but I don't think it makes a lick of difference if your beer in the keg is fully-carb'd or not, so long as the keg is properly purged. In reality, if the keg is going to sit disconnected for a while, I think your main concern is to make sure the poppet valves are well-seated/sealed (30-odd psi for a 5gal corney.)
Beyond that, avoid wild temperature swings--the only allowed one is downward prior to serving.
It tasted a bit acidic which when I tasted it uncarbed it was delicious. Am I doing something wrong? Should I have just let it sit under pressure?
Acidic off-flavor would indicate an infection:
https://www.morebeer.com/content/homebrew-off-flavorsIf it tasted ok just before kegging, perhaps the keg wasn't as sanitary as it could've been?
"You can't sanitize dirt." The most-common places the crud can hide are in the liquid dip-tube, in the dip-tube posts, any of the seals, and just inside around the lid (where you can't see well.)
A carboy/keg washer and a big tub of PBW are a solid investment if you have many kegs. One properly-sized tubing brush and a big, bristly bottle-brush will work on a budget.
To add to the conversation in general, when it comes to pin- vs ball-lock, stick with one style, but get what you can afford if prices are wildly different. My preference is for ball-locks primarily because of tools. A 7/8" deep-well socket-wrench is all you need to do gasket maintenance, whereas a pin-lock requires a modified socket to clear the pins. I've read recently that it is possible to swap posts, but I obviously can't confirm this.
Also read this recently: PepsiCo used ball-lock, and Coke used pin. A recent shift to bag-based dispensers means that reasonable used corney kegs can be had for $35-$45.
On the subject of CO2, I suggest taking a look at Northern Brewer's gas supplies. I recently installed a 4-way distribution block in my Danby keg fridge. Managing 3 corney kegs plus a beer gun is so much easier with independent shut-offs, removing all the Ts reduced the risk of leaking gas, and the tubing mess is greatly reduced.