If you won't need it, delete it - why not? If you're going to use it later, save it.
ZIP? Sure, no problem. Command depends on exact utility you use (and operating system). The easiest way would be using one of ZIP GUI versions (for example, WinZip or WinRAR or ... on MS Windows). ZIP command line help *should* be available if you type "ZIP -h". It will show you that file is to be added using such a command:
> ZIP scott.zip scott.dmp
If you decide to transfer dump file to another computer (because, for example, the one you are on doesn't have a ZIP utility installed), don't forget to use BINARY MODE.