1. In Nightfall you get your basic skills by completing the Sunspear training courses. Make sure to talk to ALL the elementalist instructors as well as all the instructors of your chosen secondary profession.
You also get "Hero Skill Points" which can be used at "Hero Skill Trainers" - not just to get skills for your heroes but also for yourself.
That is, say you have 2 hero skill points available - you can then go to the Hero Skill trainer in Kamadan and ask for 2 Elementalist skills. This will unlock the skills on your account, (for pvp and for your heroes.) but also give them to you as if you had paid for them at a skill trainer.
Note, each hero skill trainer has a different set of skills for "sale".
The trainers in Kamadan, Sunspear Great Hall and the Command Post also offer the Sunspear PvE skills. (one per profession.)
Note that you can't put the PvE skills on your heroes.
Also, you can buy skills from trainers as per usual. Not just from LA, but in most of the Nightfall outposts. It's cheaper to accumulate hero skill points and get them for free though. Check the list of hero skill trainers here:
http://wiki.guildwars.com/wiki/List_...skill_trainers to see the list of skills you can get for free.
You CAN also go Lion's Arch and grab the free skills offered as quest rewards in prophecies - but only from Kryta and onwards. (IMHO, it's not worth the extra effort just to save some gold, but if you're really strapped for cash, go ahead.)
2. You can travel to Kaineng Center and Lion's Arch as you please, when you have unlocked travel to the mainland.- there's a quest for getting both to Prophecies and Factions. I suggest just taking it slowly and completing the Istani storyline before you go though.
However, if you're impatient, you can buy a "run/taxi" to the consulate docks, where you can pick up the travel quests. This may however permanently gimp your character as you could be stuck without meeting the requirement for a secondary profession. (As I recall, you must be a certain sunspear rank for that and well, higher level chars aren't allowed to take sunspear bonuses, so they can't advance in rank.)
So, only do that if you are aware of the risk.
3. You can always ask a trusted friend or guild mate for help, but otherwise, you can try running the game on two pcs or even running two copies of the game on the same machine (you need to use special software for that though and that's not officially approved by or supported by Arena.net. - check the tools section of this forum for more info.)
[edit, ninjaed]
I think that they meant transfers of items across accounts, not within the same account @ Drec Sutal - though your advice is good for shared storage on same-account characters.