I always, always, always play a healer in MMOs, ALWAYS.

I know there is no set healer, you pick and choose skills as you like. I am also aware that the Templar is the "base" class for a basic healer role. However, in the leaked video, I noticed something strange. As a Sorcerer, that guy did not have one healing spell in his class list. Okay, I get he is just a starting Sorcerer. We also are told that the three starting trees are unique to each class.

So, if I do not play a Templar, who starts with a healing tree, where do I get a healing spell from, if I played Sorcerer?

You'd get healing from the Restoration Staff tree, which everybody (Templar included) has access to.

Everybody can heal with the resto staff. Only the Templar can heal without it, based on what we know.

It was my understanding that you could cast spells without a staff in your hand. Example was, you could cast a fireball while weilding a two handed sword.

It is similar to GW2 insofar as you can only cast abilities from weapon specific trees with those weapons out. I can only use a 2h weapon attack with a 2h weapon. Restoration staff is the same way.

However non-weapon abilities can be used regardless of what weapon you have out. Of the class skills, only the templar has a healing non-weapon tree. Unless there are heals in racial or PvP or quest trees, only the templar will be able to heal with a non-resto staff out.

As far as we know,

You can have 2 sets of weapons at use that you can switch even in combat.

You could have restoration staff equipped and then when you need you can switch to ie. Sword+shield and play as a CC shield bash/shield charge style of player (example) and when you see people low hp, you change to resto staff and do heals again.

Or you could change to destruction staff and start DPSing, but as healing takes mana its best to mix healer with stamina based attacks.