If you have a static address from the ISP then yes, theoretically you can use static for both routers. With regard to the Wan/Lan port, you will have to see what works best.

Is there any point in you connecting the PC directly to router2 after you have enabled DHCP on it to see if the problem really IS related to the wireless part of the connection? Run it for a test period whilst hard wired to the router and see whether you get issues.

Have you tried ALL of the channels in the range? Could be a local bleed from another wireless source disrupting your setup.