1- Any class should have you covered in any game mode but there are some that will excel at certain things, which may/may not get nerfed soon/a lot later/never. Since pvp is your main thing, I recommend trying each class in pvp to help you decide what o main. You can hop into pvp right after tutorial. Everyone in pvp are set to max lvl and get the same max lvl gear, and all your talents fully trained. You just have to select which stat distribution preset you want and put together a build.
2- Levelling gives you a chance to take a casual stroll through the world and enjoy some stories playing out in each zone, and I personally find it quite enjoyable. But "need to level the long way to learn your class" only applies to people who would boost to max lvl and decide not to figure out how to play the character, and then join harder content where they need to be at least half competent. If you boost up and take a little time to learn, then that's fine.
3- If you think in terms of WoW servers, there are only 3 servers in GW2 (megaservers), EU, NA and China. The "worlds" in WvWvW are like alliance and horde, except there are a lot more than just 2 factions. When you're not in WvWvW, every one on a megaserver plays together with others on same megaserver. The game will just make more copies of each zone when a zone gets overcrowded. WvWvW is like an Alterac Valley with 3 factions fighting, and runs a week-long match then a new match starts each week with new opposing worlds. Look into which servers/worlds are active/inactive for this, because it will matter if you plan on playing this mode.
5- You can earn gold in game and convert into gems. (for buying bank slots etc)
6- The expansions are very much worth it imo.