Sync iOS Apps to iTunes - Questions on how exactly this works...

Question

I'm going to put my questions up top, but my understanding of the current system is below, and may be relevant to the questions, if you'd like to read through it.
How can I back up / restore a SINGLE app, including its data (e.g. a game save file), to either iTunes or the cloud... or anything else for that matter. Does syncing an app to iTunes serve this purpose?
What IS the purpose of syncing an iOS app to iTunes? Does this sync include the data stored on my iOS device? For example, if I have a game in which I've made progress, is this progress stored on both my iPhone and my Mac once I've synced the app to iTunes?
If data IS synced along with the app, how is this data managed? Say I have two iPhones, both with the same game but different progress in each. If I sync iPhone A with iTunes, then sync iPhone B, will iPhone A's data overwrite iPhone B's? Or are there two versions of this app floating around on my mac?
If data is NOT synced along with the app, why on earth would I want a bunch of huge storage-hogging iOS apps that are identical to what I could download from the App Store taking up GIGABYTES of space on my MacBook's SSD?
And finally, should the answer to question 4 be "there is no reason to store 42GB worth of useless apps on your 256GB SSD alongside your already gigantic iOS device backup files," how would I go about removing these apps stored in iTunes without iTunes trying to delete them from my iOS device every time I want to sync some TV shows or podcasts?
My Understanding So Far:
Of the many things Apple has addressed and improved upon over the years, backing up iOS app data has strangely not been one of them. As I understand it, the only way to back up an app, including its data (e.g. the save data for a game), is to do a FULL backup of the ENTIRE device. The only way to restore an app, including the data that you backed up, is to restore the ENTIRE device, all other apps included, to a previous state.
The driving force behind these questions is that I'd like the option to delete an app from my iPhone when I'm finished with it - but I'd also like the option to re-download it in the future and pick up where I left off. In a perfect world, all these apps would automatically sync through iCloud or GameCenter, or at least have that option to "upload to iCloud" or "restore from iCloud." Even with these apps, I'm not entirely sure where the backed up files exist - somewhere on my iCloud drive separate from my iPhone backup, photos, contacts, etc? Is there a way to see a list of apps that are storing things in my iCloud drive, and even manage this data?
So if I wanted to back up an app's data that does NOT automatically back up to iCloud, it seems my only option would be to install one of the many 3rd party Mac <-> iOS data transfer apps, and copy the contents of the "Documents" folder to a designated directory on my Mac. Then I could delete the app off my iPhone. Say in the future I re-download the app - I'd use the same data transfer app to copy the backed-up data to the re-downloaded app's Documents folder, and we're back in business. The only downside is that if it's been a while and the app has undergone updates, this backed-up data might be corrupt or no longer relevant. Plus, it's kind of a hassle.
When I discovered iTunes was syncing my apps to my Mac, I thought it might be serving as a way to back up my apps, data included, to my computer. Okay, it seemed like a little overkill to sync the whole app along with the data, but when I discovered that you could UPDATE the apps within iTunes, I thought apple had solved the problem of storing backed-up data for out-of-date versions of an app - simply update the app in iTunes, it does what's necessary to your backed-up data, and when you want to put the app back on your iPhone, voila! Your old data's there, AND you've got the most recent version! But apparently this is not at all how iTunes app syncing works.
As I NOW understand it, when iTunes "syncs" an app to your Mac, it includes only the app's core data - the same as if you'd just downloaded it from the App Store, and it does so for EVERYTHING you've purchased, ever, whether or not it's on any of your iOS devices. I can see how this could be convenient if you live on a farm and want to restore an old app to your iPhone without an internet connection, but I don't think it's worth, unexaggerated, a FIFTH of my hard drive. Worse, I can't figure out how to get rid of them.
TL;DR
So, if you're still with me, what is the purpose of iTunes App Sync, and if it's as useless as I think it is, how do I get rid of it for good?

Answer 1

You can upgrade to Snow Leopard and skip over Leopard, and only upgrade to Lion later if wanted/needed. snow Leopard specs/requirements below.
http://store.apple.com/us/product/MC573Z/A?fnode=MTY1NDAzOA
Stedman