Why would it need to play from the iTunes on the computer when it is fully loaded with songs and is charged/charging on the shuffle charging dock?
Why? Because that would require an ongoing transfer of data from the iPod to computer, which would require more complicated hardware and programming, which would increase the size and cost of producing a shuffle. If it is treated as just a known playlist, data transfer is only needed when you manually or automatically fill it. That's simple.
It tells me 0 items, 464 KB available.
That is probably outside of iTunes. The files are invisible, so it is 0 items. The files still exist, so they take up space.
Will the songs be erased from the shuffle as soon as I select 'Erase and Sync'
Yes. An iPod shuffle can only be associated with one computer at a time. If you want to get songs off of it, you need to use a third party utility (search using Google to find one) which can transfer the songs from the iPod before using iTunes to +erase and sync+.