DNS server at router level vs. computer level

I've done it both ways.

1. Your router typically caches the DNS entries it requests, and you only need to set it up once. Practically, after the first lookup it should be faster. Its also simpler, since you only need to set it up in one place. I don't use my ISP DNS servers so I alwyas set it up here

2. no - your PC will simply ignore the router's dns server

3. Your router's ip address IIRC. I used to run a seperate dns server inside my network at one point, and I simply used its ip address

The OS always has the DNS server written in but it can be the router IP, and the router then goes to your ISP's.

Or the OS can point directly to a DNS server (your ISPs or somebody elses like Google offers a DNS server).

It should be faster to give your OS your ISPs or Google's DNS server, rather than your computer making a DNS request to your router and for your router to then contact a DNS server.

I can see my DNS servers in my router but if you can't then you can call your ISP and ask them. Or use Google's. 8.8.8.8 or 8.8.4.4

I agree it should be a little faster, but I doubt that you notice.

But it is easier to set it to the Router and then let the router release all the information to the client(s) ( DHCP ). If you have a second computer the next one is plug and Play.