IPod Touch won't sync, false "this cable or accessory is not certified" and several other errors

Question

Helping my dad long-distance with his iPod Touch 5th generation, running 8.1.1.
He's having several problems trying to sync the thing:
1) "This cable or accessory is not certified and may not work reliably with your iPod" error, even though he's using the cable that came with the device, when connecting to his Mac. (This happens with both certified Apple cables he owns.)
1.1) He's unable to take screenshots of this error, even though he can take screenshots of any other screen.
2) Won't charge when connected to his Mac (does charge when connected to his 5w cube).
3) Connecting to Mac dones't launch iTunes, but does launch iPhoto.
4) Sometimes, even after launching iTunes manually, the iPod doesn't show up.
5) We we can get the iPod and iTunes to talk to each other, he gets 7/8ths through syncing, then gets the error "Some of the videos in your iTunes Library, including the video IMG0925.jpg, were not copied to the iPod because they cannot be played on this iPod." — yes, the "videos" that won't "play" on his iPod are all JPEGs.
6) When clicking [OK] to clear problem #5, it's always followed by "iTunes cannot back up the iPod (device name) because an error occurred." Even though it was 7/8ths done before the error occurred.
7) Issue 5 and 6 occur when connected to the Mac over wifi too. (We've tried with wifi backup both off and on.)
7) He's randomly prompted for his iCloud password at least 3-4 times a week. Entering it doesn't make this problem go away.
8) Tried to update to 8.1.2 (hoping it would fix some of these issues), but after tapping [Agree] in the overlay screen, he's taken back to the T&C screen with [Decline] and [Agree] buttons at the bottom, and NOTHING happens.
So we he back up via any means, he can't upgrade, and we can't wipe and restore because he'll lose a month's worth of updates to calendar and address book.
I'm know my way around Mac and iOS, and I'm stumped. Anybody got anything?

Answer 1

#1
- Try another cable. The cable for 5G iPod (lightning connector) seems to be more prone to failure than the older cable.
- If a 5G iPod               
Iphone 5 lightning port charging problem - SOLUTION!
- Inspect the dock connector on the iPod for bent or missing contacts, foreign material, corroded contacts, broken, missing or cracked plastic.
- Make an appointment at the Genius Bar of an Apple store.
  Apple Retail Store - Genius Bar
#1.1 n/a because the errror message overrides it
#2 see #1
#3 iOS: Device not recognized in iTunes for Mac OS X
But could be caused by #1
#4 Covered by previous ones
#5 Obvious jpegs are photos and thus will not sync as videos. Also see:
iTunes: May be unable to transfer videos to iPhone, iPad, or iPod
iTunes: Frequently asked questions about viewing and syncing videos
#6 iOS: If you can't back up or restore from a backup in iTunes
First #7 See #6
Second #7 You have so many other problems resolve those first
#8 Resolve other problems first