1. Free Companies are indeed the guild system in this game. As for necessity of having one, it depends how inclined you are to have a social circle. There is not really "need to be in FC" content, now that people can purchase even apartment rooms outside of them. There is also Novice Network, a sort of chat channel dedicated to help new players. You need to be invited to it by a mentor (those folks with fancy crown icon in their name), usually asking in the /shout in any major city should catch at least someone's attention.
5. Apart from what previous poster said, while you can start PoTD from level 1, if you actually do the first class quests you find yourself on about level 7 in no time. And I too heartily recommend playing every dungeon (maybe not each of the first three) at least once on every class when you come on their level, to keep a current understanding how your skills work in context of usual party play. The PoTD playstyle is quite different for most part. Also I seem to recall that up to level 47 or so, if you have one class on high level and thus the experience bonus for leveling other class, you pretty much gain one level from one dungeon run. Choosing to level through dungeons is thus as valid choice.
7. For healer class, unless you're wanting to shoot into the peak endgame content right on this minute, the healer class you choose doesn't matter that much. They are all valid healers in most of the content and what matters more is how you like their peculiar play styles. It's not even bad idea to dabble a bit in all three to see which you like the best. Also as said the SB is just around the corner and the classes are bound to have changes and while their core ideas should stay the same, the "flavor of the month" for the peak performance might shift. But for nearly all the content, there is not one healer class that's more or less wanted than others (same for other classes as well, actually).