I want to build a shed that is 6' x 14' and 2 sides will be attached to the house. One 6' side and one 14' side will be the sides that are attached. My first question is, will this be okay if two sides are attached? Seond question is, I currently have an exposed aggregate patio where it will be built on top of and wanted to know if I pour a foundation for the shed how wide and high it should be above the patio? Third question is, what should the height be on the 14' side where the roof will start? Also, can you give me a clue as to how much this will cost as a DIY project?

Thank you

You don't provide all the necessary info for answers but here's a little.

A roof staarts on the wall that bears it up. so assuming that you want the water to drain away from the other wall where it adjoins the house, and assuming that the bearing 14' wall is eight feet high, you always need a minimum pitch of 3/12 for shingles, (but more is better, what is the pitch on the rest of the house?) since you have a run of six feet, the pitch would bring you up another 1.5'

Then, if you figure that you would use 2x6 rafters, the roof line would intersect the wall of the house at nearly ten feet above the sill of the oposite wall.

How high should the roof be for a 7' high wall?

Well, let's think about that for awhile. I gave the answwer for an eight foot wall and you want the answer for a seven foot wall. That's one foot less, right?