|My question is can the 2nd downstairs router also use the LAN connections.|
Yes it can, Set up the "main" router as normal. Configure the second router downstairs in bridge mode or "client" mode depending on what the manufacture calls it, with DHCP disabled and connect to the first router via wi-fi.
You can then connect your TV and Entertainment centre to this router via cable by plugging into one of the LAN ports. They will get DHCP addresses from the first router upstairs. .You will need to use the Entertainment centre to configure the 2nd Router. What you wont be able to do is connect to the 2nd router vie Wi-fi as it will be in client mode. Any connections to the 2nd router must be via cable.
So the second router downstairs needs to be one that can do client mode. Most do but not all. The routers manual will give to exact details of how to set it up.