Copper.
RJ-45
Cat 5E
Cat 5E or Cat5
stp cat-5
If you can use fiber optics. If not try to use CAT-5e at least, CAT-6 is recommended.
It depends on the type of LAN; the most common cable in a LAN is UTP cable. In older LAN types you could also use coaxial copper cable. For UTP cable that would be Cat 5, cat 5E or above for most LANs.
To the switch the router is just another host, so it connects with a straight Cat 5 or Cat 6 cable.
Cat 5, Cat 5e
Rj 45 refers to the ends of the cable. The type of end it has. The cable itself is cat 5.
Yes
The modern Ethernet cable is a Category 5 UTP cable, with an RJ 45 connector.
Cat-3 is the most common and least expensive.