You can login with up to 1.7.3 clients but the server itself is still 1.6.2; you can just connect using it.
No, that'll be implemented later. The Bungee system Aikar implemented allows for that, I've been connecting with 1.7 since.
Oh darn, that sucks. It looks like you have been logging in from time to time - does that mean you have another computer you're able to use? (If so, I highly suggest checking out R0bbieJo's smp4 winter project, it's absolutely AMAZING.) Anyways, I hope what ever is breaking your computer gets fixed soon, and wish you the best of luck. Not in this update, that will be added later. Yep! We all know you can't demand exact time from Aikar, or he'll make it last 3 more years.
I was able to log in until about four or five days ago, or so. Clicking the multiplayer button just crashes minecraft. I tried to update java, but it was already up to date. I'll just delete everything related to minecraft and reinstall it.
Can't wait for them new biomes! Gonna enchant my fishin' pole and catch some of em' nice fresh salmon!