HELP!!!!!

You can transfer purchased songs from your iPhone into the iTunes library of a computer you connect the device to, provided that library has been authorised to your account. Once the files are on one of your computers you can transfer them to any others as you wish in the normal way, via network shares, external drives, memory stick etc.

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I bought music on my iphone, but it didn't show up on the itunes library on my computer, and I want to put the music that I bought on my phone on the itunes library, how do I do this?

connect your device and right-click or control-click it in the iTunes Source list, then choose transfer purchases from the shortcut menu that appears.

Just connect the iPhone to your Home Sharing computer, run iTunes, and go File Menu → Transfer Purchases from "Your iPhone Name". It's not a bad idea to do this on more than one computer so you have redundant copies of your purchases too.

Oh, and about getting them to come up on Home Sharing, the best thing is to make a playlist and drag you purchases into it. Then as long as the playlist is shared, it should come up properly.