Ok sorry if this is the most basic question in the world but for years I have needed more ethernet ports in my room and my whole house is wired with 1 ethernet port in each room, I also wanted to be able to plug into the room ethernet port with another router to get more plugins and that wasn't possibe I don't think. So can you plug a switch into this and have more ports with just as much speed?
Yes. In fact, I have a gigabit switch connected to my 100 router. All the gigabit computers are connected to the switch. When two of those computers want to talk to each other, they bypass the router and talk at gigabit speeds (sadly, well short of theoretical, but much faster than 100). And of course they talk to the rest of the LAN and the internet just fine.
Yes. Things would be quite complicated if the internet had a router somewhere with 1,000,000,000 ports in it that every device in the country had to connect to.
Yes, this is how a lot of enterprise networks are set up actually. There is typically a border router which is the gateway to the internet, then switches section things off into their own collision domains.
So can you plug a switch into this and have more ports with just as much speed?
If you're referring to LAN speed, then yes, assuming the switch's speed is at least the same as the router, and it is a non-blocking switch.
Yes. You can connect as many as you want as long as they are downstream to add more ports and extend the client base; albeit taking into account limitations and constraints of CAT/Ethernet IEEE standards and practical signal attenuation.
If you added switches upstream it would be for whole different set of reasons that is beyond the scope of this question.
To better illustrate I share a diagram of the Home 'Media' Network I put in place almost a decade back that illustrates Switches, Routers & Wireless APs/ Routers. It will help you plan and visualize how you wish to add switches and equipment to extend your network and ports.
I will write more about it later today. I figured this should help for now.
Here's another one from a fellow (Sunil) here on this forum.