Hi, this may take a few conversation rounds but here you go, I'm glad to do it!
Yes of course you can stream Pandora from your iPad to your stereo, I do it with my iPhone
all the time, as long as you have a good data connection, meaning the iPod touch can open safari and browse, Pandora will connect and play. I'm using the headphone jack, but I don't think that will matter if your Alpine supports the bottom jack.
As for iTunes. You can only sync with ONE library on ONE computer, but you can sync as many devices to that ONE library as you want. I sync several iPods and an iPhone to one library.
Essentially you need to copy over all the content from your old library to the new one, then re-sync you iPod. It's going to tell you that it needs to "erase" everything, which is true, but it's just going to put it all back on.