how do i upload my dropbox music library to my ipod nano without losing the music already on the nano. what app?

You need iTunes running on a Mac or Windows PC to sync songs to an iPod. There are some alternative music manager apps that can sync songs to an iPod, but I don't recall "Dropbox" being one of them. It may work with iPod touch (which is an iOS device like iPhone and iPad).

For your other question, you need to off-load songs from the iPod using a third-party method or utility. iTunes syncing is generally in one direction only, from iTunes library to iPod. You cannot use iTunes to transfer song files from iPod to computer (except for songs purchased from the iTunes Store). However, there are third-party methods and utilities that can transfer from iPod to computer. If you do an Internet search on something like "ipod music transfer," you should get some links (including a useful article by CNET on the topic). And "Senuti" is one of those utilities.

NOTE: Songs previously purchased from the iTunes Store can be re-downloaded at no cost, from the iTunes Store Purchased screen.

Download your past purchases - Apple Support