If you are going through his router/firewall he could conceiveably monitor what you access. Although usually only high spec routers keep such detailed data.
He could also run a program on his PC to watch the data traffic on the LAN (IE your PC's data). This could provide much more detailed info about what you are doing on the internet and enable snooping on your email.
He could, if you have set up your PC sloppily, access it and/or control it, because your PC would be on the same LAN as his and you are both on the same side as the router/firewall.
So in summary: yes, its possible, and you are right to be concerned but it's difficult to give an exact answer without more details of the hardware,