Why doesn't my iTunes content show in Library? Also, How can I sync music purchased on my iPhone to my PC's iTunes Library?

Question

I have been having several annoying problems with iTunes for the past several months...
1) Library content not showing after folder relocation:
First, in order to free up space on my C drive, I wanted to relocate my iTunes folder to a new 1TB hard drive (F) I installed. I did so according to Apple's instructions online, but despite setting the new location to be my library in my iTunes preferences, the content never shows up in the iTunes Library in the actual application. This is my most annoying problem, so please someone help me to resolve this! Thanks.
2) Albums purchased on iPhone 5 only sometimes sync with PC
I have purchased a few albums on my iPhone 5 and only some of them have synced to my PC when I connect my iPhone via USB. They don't even appear under the "Purchases" playlist in the iTunes Store. So, I have content right now on my iPhone that I can only access via my iPhone, and some of the music has gone missing. One or two tracks from albums are not there despite me purchasing full albums at a time... This is also pretty dang annoying and prevents me from trying a solution I'd looked up to fix my third problem...
3) Album artwork mixed up/mismatched on iPhone 5
This is pretty self-explanatory. Ony day my album artwork decided to play musical chairs. So now, for example, it shows Andrew W.K.'s bloody face when I listen to Zedd, and shows Skrillex when I listen to Symphony X. I read online that if you desync your content on you iPhone so that none of the music is there any longer, and then resync content from your computer, it will fix this issue. I'm hesitant to apply this solution until I can fix the ones above though, because I don't want to lose content that I have legally paid for.
My final problem:
4) Apple charges $20 for a support phone call for iTunes
Seriously, WTH? I hope the community can help me out. Thanks all!

Answer 1

1) The best way to relocate the iTunes library folder is to move the entire iTunes folder with all subfolders to the new path, then press and hold down shift as start iTunes and keep holding until prompted to choose a library, then browse to the relocated folder and open the file iTunes Library.itl inside it.
If you've done something different then provide some more details about what is where and I should be able to help.
2) Purchases on the device should automatically transfer to a Purchased on <DeviceName> playlist, but it my depend a bit on whether automatic iCloud downloads are enabled. If there is a cloudy link then the transfer might not happen. You can use File > Devices > Transfer Purchases. In iTunes you should also check out iTunes Store > Quick Links > Purchased > Music > Not on this computer.
3) Backup the device, then immediately restore it. In some cases you need to add a restore as new device into that equation. Obbviously not to be attempted until you're sure all your media is in your library. See Recover your iTunes library from your iPod or iOS device should it be needed.
4) I believe there is complimentary 1 incident 90-day support with hardware purchases, but no free software support for iTunes itself. AppleCare gets you a different level of support.
tt2