CROSSOVER
Im in CET too ;)
An HDMI cable is not designed to connect two computers together.
Easy transfer cable
In order to connect to computers together using Ethernet you will need to use a cross-over cable. This will then allow you to share files and resources.
You can connect two or more computers using the following cables: Network cable USB cable Serial (used in old computers) Parallel (used in old computers)
Best way is to connect both computers to the same computer network (within the same router, or switch). You can also connect them directly using a crossed patch cable, or wireless by creating an ad-hoc Wi-Fi connection of these two computers (if both have Wi-Fi adapters).
It depends on model. Some modems come with a wireless router. If yours has wireless interface, you will able to connect your computers wirelessly. Usually what you have is a modem with one LAN port. If you want to connect your 3 computers to the same modem you need to get a wireless router. It will allow you to connect your computers using wireless or cable. Switch in such case might not work because of internet provider policy.
I believe that it is possible to connect to computers to one monitor. I have worked with brand new LCD monitors with two inputs - one DVI and one VGA. The monitor auto-senses which port is being used. So in theory, use the auto detect button on the front of the LCD panel to switch between computers.
If you are using a crossover cable, simply assign static IP's to each machine (192.168.0.2 and 192.168.0.3). If using regular network cable, you will need to use a network switch or hub to connect them together, still using the static IP's for each machine.
Depends on the way you want to connect them. Most probably you want to connect them using network interfaces. In that case you have to use cross-over cable. Straight cable, the sort you would use to connect your computer to a wall network socket, will not work.
yes you can
You would need what is called a crossover cable. It is basically an ethernet cable with 2 of the wires swapped on one end. This swapping is usually done inside a switch but has to be physically done on the cable if you are trying to connect direct. You also have the option of using special USB cables to connect computers directly.
Most computers don't like it so much if you try to connect them together directly with an Ethernet cable. Your best bet is to purchase a router and connect both computers to that. Wait, without cables? If they both have wireless capability, you can create an ad-hoc network between the two. Otherwise, good luck trying to connect them.