Question 3:
1.) Computer A trys to communicate with a Computer B not on it's subnet.
2.) Computer A sends a packet to it's default gateway
3.) The gateway then determines how to get to Computer B (routing)
4.) At the destination network, the switch arps for the mac address associated with the desination IP address in the packet.
5.) Computer B reverses the process to send back to Computer A
Question 1 should be answered by my answer 3.
Question 2: Subnets conserve IP address space. For a point to point connection, why waste an entire classfull network (/24) when you can use just a portion of that classfull network?
Edit: I'm not sure if you are asking how routing takes place, but if you are I guess I failed to answer it so I will attempt to do so now.
Routing is based on, you guessed it, routes. These can be manually configured or dynamically learned. You might think of basic routing like you would a DNS hierarchy.
ip route network1/subnet via interface 1
ip route network1/subnet via interface 2
ip route 0.0.0.0 0.0.0.0 via interface 3
In this example, the router knows about two directly connected networks that it can route to. The last line is a "catch-all" which basically says, if all configured/learned routes are no good for the destination I am trying to reach, use this one and let someone elses router find the destination.
As for link-state and hybrid, those types will handle routing updates differently but it all boils down to the same thing. They know about directly connected networks which they can then let other connected routers know about. If "all else fails" they can use a default route and let someone elses router find the destination IP.
