IS there a way to transfer my emails from my old host? I can download them from my old provider via ftp, can i ftp them into a folder so they all appear in my inbox on the network solutions server?

You don't have FTP access to the Network Solutions mailserver, so the best way to transfer the email would be to login to the Network Solutions webmail interface, and setup your old provider as an external POP3 account in the settings. This will download all the messages via POP3 to your current inbox.

I need to change my domain name from pointing to the current host to network solutions to get the email to work on NS, I assume this will kill my connection to the current host when I do this. Any suggestions for this? open gmail pop3 account and transfer files to gmail then do the same for NS?

That would work, assuming GMAIL has the same POP3 transfer funtionality. I would double check with your old host though, usually even if DNS is switched the mailbox stays active (however it would not be able to receive due to a changed MX record). Most likely you would still be able to access it via an IP address and username/password.