1)Your router will work with alliance
2)The internet is registered with your PC's/router's MAC address,so you can't plug the cable into another PC cause then the internet won't work.
But with a router things are very easy,you can have the router copy your PC's MAC address or alternatively get your router's MAC address registered into their system...Anyway you choose you could run as many devices as you like,so don't worry.
3)My connection is pretty great,much better than that sucky BSNL!
used to have downtime of a few minutes every couple of days(a few mins did not bother me,esp coming from BSNL whose connection seemed to go out for weeks),but now it seems to work great...but eventually it depends on your local cable guy,cause he is responsible for your internet!