Two handing a weapon and removing a hand to cast works fine (taking a hand on or off a weapon is a free action). This works fine regardless of if it is a longsword(one handed) or a great-axe(2 handed).
Bear in mind that at 5th level the arcane duelist can use the hand holding his bonded item to perform somatic components anyway.
All bard spells have verbal components. The bard needs to speak in a loud voice to cast spells regardless of if the spell also has a somatic component or not.
Yes, when you take a first level of a class* you need to know if it's an archetype or not.
(not actually true, but if you follow it you'll never be wrong.)
It just occurred to me; can you actually start a new character at level one as an archetype class? Have I misread this horribly?
Unless you are using the retraining rules, you *have* to start as the archetype at level one.
If you are using the retraining rules, you can wait until the character would be affected by the archetype and then choose it - you get a bonus feat at level one so this doesn't make a difference to you, but for example some fighter archetypes only become different to regular fighters at level 2 so they can choose that archetype when leveling to level 2.
You can also use the retraining rules to add/remove/swap archetypes later, but that takes time and costs gold as per the retraining rules.