Yes, you can connect a wireless router into a modem router to set a wireless network. You could also use a wireless access point rather than a wireless router.
If you use a wireless router, you will probably need a cross-over ethernet cable to connect the 2 routers, though some have auto-sensing uplink ports and can use a normal cable.
You can't view emails on one pc from another in a home network unless you have a mail server, which is what you have at work. There are a number of work-arounds, though. One option is to use webmail - many ISPs have a webmail option. The other is to set your email clients to leave email on the server rather than download to a pc, so that any pc can access them. In both cases you can decide between yourselves a protocol for removing them from the server.