Should this story contain lemons (or should it be more of a fade to black scene)? Yes, the story should have lemons.
When should their relationship go to another level? (IE, How far and when?) Well, since you already have them kissing, for "light petting" I think maybe 2nd or 3rd year, for "heavy petting" I don't think you should do that until at LEAST Harry's third or fourth year, any younger than that is just a little odd. I leave it up to you for after that however.
What do you consider over powered Harry? An over powered Harry is a Harry that walks into a room and everybody dies in 30 seconds. He should still be able to get injured, but for the most part (particularly in his younger years) to fight Death Eaters he should have some trouble for awhile, and then when he's older he gets the strength to fight Voldemort.
What do you think should happen at Beauxbatons during the school years (1st, 2nd, and 3rd)? I don't particularly want to see one thing or the other, surprise me! :D
Good story! Can't wait for the rest! Cheers.