How balanced is the PvP in its current state?(Are some classes blatantly superior)
In GW2, rather than discussing classes, it is more appropriate to discuss roles. This is due to the fact that unlike other MMO, there are no specific roles that fit a class. However, do take note that some classes fit some roles better than others (but only by a bit).
Since gear apparently does not matter in PvP in this game(based on the video I watched), what exactly separates a good player from a bad player. If I get into a 1v1 engagement with a player in WvWvW how exactly can I out play my opponent? GW2 seems to have less skills to use as opposed to other MMOs. Is it just generally which ever person gets the jump on the other? Or is there a large window to out play people?
Firstly, PvP and WvWvW are different. In PvP, it is basically even numbered fights (from 1v1 to 10v10 depending on lobby or 5v5 if you play ranked). In WvWvW, you need to find out whether your server has coverage during certain timezone. You may find yourself 10 v 80 at one time or maybe 80 v 10 at another.
What separates a good player from a bad player? Skill rotations and their use of dodges. As you mentioned, GW2 has much lesser skills to use compared to say WoW. So it is much more important for a player to know when to use a skill. For example, a stun is very useful skill with a high cd but use it on someone with stability and you just wasted your skill (Stability is a buff that negates most cc ability).
Advantage is always given to the person who jumps on others first. However, a single dodge may, as mention before, blow a big cooldown skill and may instead give the advantage to the person being jumped on.
How do Warriors/Necros fair in PvP and what exactly do they bring to the table?
As mentioned before, it is not classes but the roles you wish to bring that matters. Necros may fall off a bit from meta but terrormancer is always good addition. Warriors have many builds to choose from.
How important is crafting in this game and how profitable is it?
As a lot of people mentioned, the only reliable way to get Ascended gear (BiS armor and weapons) is from crafting. It is not as profitable as it used to be but some recipes may net you some gold.
Does Light/Medium/Heavy armor function like it does in regular MMOs?
It is totally different. A glass cannon guardian (heavy armor) will have much lesser sustain than a bunker engi (medium armor). And the class with the most health is Necro (light armor) (if you count in life force pool and lich/plague form) . So it's very different from regular MMO.