If router 2 gets internet from router 1 then yes you can plug an Ethernet cable from router 2 to a device.
As far as speed that completely depends on your setup.
The ideal setup for this is as follows:
ISP source (dsl, coax cable, fiber) -> modem or media convert (output will be Ethernet) -> Primary router -> ethernt to PCs near primary router and Ethernet to second router -> Second router configured as access point -> devices connected to second router.
Your second router should be setup as an Access Point because otherwise devices connected to primary router will not be able to access shared files/printers behind the second router (it will work going from router 2 to router 1 but not from router 1 to router 2). Let me know if you...