Are dragons able to wield weapons?
And to be more specific, can a spellcaster cast Form of the Dragon and then grab a weapon and fight with it? (appropriate size and spellcaster have weapon proficiency)
I would say yes. Dragons can wield weapons though its usually better for them to use their natural weapons / spells / abilities.
Again yes. (Because it is awesome!) again the natural attacks would usually be a better choice. There are 5 of them after all (for Form of the Dragon I).
I believe that dragons have the equivalent of opposable thumbs, so I'd say yes. But as Avianfoo pointed out, why? Dragons Natural attacks rock! Also remember that anything on your person melds when you use a polymorph spell/effect, so you will need either a polymorphic bag to stow your weapon in, or you will need to drop your weapon, cast the spell, then pick it back up. The same is true for spells - you either need the eschew materials feat, or you have to drop your spell component pouch, cast the spell, then pick it back up.
I would say because the spellcaster will need a new way to bypass DR and also why not take the sweet bonuses and epicness of being a dragon alongside with the devastating power of your primary weapon?
Also this is one of the coolest thing around. A dragon with a longsword? How awesome?
And what about strength bonus?
While using greatsword, for example.
Twohanded weapon: 150% Strength
Tail slap: 150% Strength
Wings: 50% Strength
Bite: ???
And what about size of weapon? Can i hold my weapon (Medium) in polymorphic pouch, and then retrieve a large or huge version of this weapon from it while in dragon form?