I have a 4 port Linksys router. Although it is probably 5 or 6 years old,
it still works great. I need more ports in the the house, and don't want to
go wireless.

Can I buy an 8 or 12 port switch, and connect it to the router?

If I do, will I still be at 100mpbs, or will I drop down to 10mpbs if I use
a switch?

Can I just run one wire from the router to the switch, and then have all my
connections go from the switch to the various wall outlets in the house?
I have a mess already, so I'd like to keep it fairly organized.

Thanks for any advice.