Is it possible for a wifi router to work without modem?
Of course it will work without a modem.The router will provide a wifi connection to your devices, and provide them all IP addresses. You can send files from one computer to another, stream a video stored on your phone to your tv or chromecast, and can print files just fine.What it will not do is provide you with an internet connection.The internet connection comes from your ISP, since it is not feasible to send data over ethernet wires over long distance you need a modem, or more correctly termed a ‘media converter” to convert the medium they provide (cable, phone for dsl, 4g cellular signal, or fiber) into ethernet (or usb) that your router/computer can use.There is an unfortunately too common of a misconception that WiFi and Internet are the same thing and are completely interchangeable words.WiFi = a communication protocol and standard that allows a device to join a computer network without needing a physical hard wired connnection.Internet = a connection from your local home network (all the devices connected to wifi and lan ports of your router) to other networks. The internet is just a collection of other people’s computers/routers/web servers.The internet and the connection to it existed well over a decade before the WiFi protocols where commercialized.
Does an Ethernet cable connection from router to laptop decrease the speed of other wifi users?
This is a yes or no answer depending on context and situation.Wired is always the best for performance and reliability.Every wired connection gets 1gbps (or 100mbps in older routers) for its speed, while the 300 mbps or 1300 mbps or whatever your router has is shared among all the current wifi users.Thus buy having a device hardwired it allows it to not pull from that shared wifi bandwidth. There is no situation where having a device hardwired will be worse then a device being wireless (assuming router and cable are functioning properly)Now here is why it is also a “yes”If you have a high performance router then it can handle many hardwired and wifi connections without slow down, however a cheaper end model of router will struggle to keep up with the demand, and thus the more devices using it in general (doesn't matter wired vs wireless) will degrade performance.This also applies for your internet connection. if you have 10 devices trying to stream netflix on a 20 mbps internet connection you are going to have poor performance.So in short, the more users you have the more performance drop you may see on your network, but wired will never slow you down more than wifi will.