Yes, it count as magical against the chosen type of foes.
It is sure that the weapon count as magical related to bypass damage reduction and so on when you apply the bane inquisitor ability to it because the bane ability grants your weapon a +2 enhancement bonus against the selected type of foe.
Overcoming DR: Damage reduction may be overcome by special materials, magic weapons (any weapon with a +1 or higher enhancement bonus, not counting the enhancement from masterwork quality), certain types of weapons (such as slashing or bludgeoning), and weapons imbued with an alignment.
In short, yes it overcomes DR/magic and can damage incorporeal foes.
Your other question can be a bit more tricky but what I suggest to you (so do not take that as a rule because what are you asking is not directly specified in the manuals as far as I know) is to follow the rule that specific overrides general and say that you can apply the bane ability to a weapon regardless of if it is already magical or not (since it does not specify anything in this matter).
Bane (Su): At 5th level, an inquisitor can imbue one of her weapons with the bane weapon special ability as a swift action. She must select one creature type when she uses this ability (and a subtype if the creature type selected is humanoid or outsider). Once selected, the type can be changed as a swift action. This ability only functions while the inquisitor wields the weapon. If dropped or taken, the weapon resumes granting this ability if it is returned to the inquisitor before the duration expires.
It is pretty obvious that there are no limitations except the fact that the inquisitor must hold the weapon in its hand. It is not specified that must be magical or masterwork or whatever.
On the contrary you can see that limitation in other abilities of this kind (where you apply special effects to a weapon):
From paladin divine bond:
[...] These bonuses are added to any properties the weapon already has, but duplicate abilities do not stack. If the weapon is not magical, at least a +1 enhancement bonus must be added before any other properties can be added.
From magus arcane pool:
[...] Adding these properties consumes an amount of bonus equal to the property’s base price modifier. These properties are added to any the weapon already has, but duplicates do not stack. If the weapon is not magical, at least a +1 enhancement bonus must be added before any other properties can be added.
Hope it helps,