you can access the internet from the 98 machine through the router. You dont 'share' the router, it sits on the network feeding all computers that are configured correctly. On the 98 machine, you need to enter the ip address of the router as the gateway in network settings and put in any relevant dns addresses.
No, he cannot save his emails onto the new pc without importing them into. If he shares the folder, C:\windows\application data\microsoft\identities\?????????\outlook express they can be imported on the xp machine if you select import messages and then say they are in a directory and browse to it.
So to sum up, yes sending/receiving on 98 machine no problem. Transfering new emails to xp machine is a bit of a pain.