The first one requires you to indicate what the person is currently doing. It can be specific or general. "When will you be done doing that?" "I will be done doing my homework in one hour." The second phrase is grammatically incorrect, but you will hear it in spoken English amongst people who know each other well. "When will you be done (and ready) to do what I asked?" "I will be done (and ready) to do what you asked in 15 minutes.". In both instances, the "and ready" would be understood. However, without it, or a similar clause, the sentence is grammatically incorrect.

And you can simply say "I'll be done with this" instead of "I'll be done doing this." :)

There's no difference in meaning. But "be done doing" is used more often. I'm not sure but I think there is something wrong in saying "be done to do"