Should connecting to a router affect speed of Internet connection?

Question

I have a Netgear router and I have connected it to two MacBook Airs that I have.
I have cable internet, a line that comes out from the wall, and which I stick into the computer using the USB ethernet dongle.
But now that I am using a router, I connect the cable line into the router and use the ports to connect to the computers.
My question is:
What is the correct IP address that should be showing?
Network System Preferences show:
Status: Connected
USB ethernet is currently active and has the IP address 192:168.x.xx
The usual IP address (when I am not using a router) is usually 185.xxx.x.xx.
Is this OK, that it's showing the routher IP address?
The reason why I am asking is that the internet speeds seem to be slower when I am on the router.
It might just be my imagination and also because I am checking the speed a lot more than usual.
Should connecting a router affect the speed of the internet?
The router's maximum speed is 300 mbps and the cable internet's speed is 100 mbps.
I have noticed that the speed of the internet with the router is very variable: about 12 - 80 mbps.
Should I not worry?
I know that the internet speed with cable internet can fluctuate a lot more than with DSL.
Thanks for any replies.

Answer 1

I am connected to the router by LAN cables. I am not using wireless. I am using cable modem.
The cable from the wall goes to the router into the WAN port. Ethernet cables go from the router's LAN ports and to the two computers.
When I wasn't using the router, the speed of the cable internet could go as high as 100, occasionally as high as 200 (100 was the advertised speed of the cable internet).
Now, with the router, it's around 30. But I have gone as high as 80 while I have been testing with the router connected.
I think I am worrying for nothing, but I just want to know generally --- does a router affect the speed (assuming it's a  router that can handle maximum speeds of the cable modem and that it's connected correctly, etc)?
I read that cable speed can depend on how many people are using it at the same time in that area and that sort of thing. I know the cable speed does vary a lot. But usually it's good during the daytime, about 90 mbps.