settings
The new iPod 2G comes with 2.1.1 firmware
No, you have to restore it, then download the new software, update it, then jailbreak it again. It sucks, i know, but there isn't much you can do.
The iPod Touch software may be out-of-date or may be too new. iPod Touch apps have been known to not open if you do not have the minimum latest version of the 2.0 software, and certain apps will not open if you have 3.0 or 3.1 software.
The iTunes software assists in managing your music and video libraries and lets you control what material you want on the iPod. iTunes also keeps your iPod software up to date so that you can benefit from improved/new features found in the latest software.
If it is an update, connect your iPod to iTunes and it should tell you that there is an update, and you have the option to download, download and install, or cancel. If it is a whole new software (e.g., 3.0 to iOS4, etc.), then go to the Apple website, find the page with the new software, and then there should be a button to buy that software from iTunes.
This ipod manage software can transfer the files from ipod to computer, ipod to iTunes, and iPod to iPod: http://www.ipodtransfer.net/how-to-transfer-ipod-file-with-ipod-transfer-software.html
I don't think so
Bugs in the software are fixed, sometimes new features are added.
No.
$229
This means you have to update your software on your iPod Touch. You have too old of a software to run the apps (you are possibly running the 1.0 software). Upgrade to at least the highest upgrade of 2.0 software.