I am getting ready to build a Patio and Landscape my yard. What is the proper slope for drainage (per foot).

Second part of same question.
My neighbor's yard is higher than mine and I also need to slope mine more away from my house. Will I need to put in a retaining wall to prevent the water flow from neighbor's yard into my basement.

On a level there are two lines where the bubble sets. I use the lines on one side or other and center bubble on the line. Just enough to let the water run off but not to fast to wash away bark etc you may have at the end.

On the grade of land Depends on how much higher of grade neighbor is than you. Do you have enough room just to grade down from your place to a place between the two houses and make a ditch for water to go to and run away from both houses?

I had a patio that was built level and I had to deal with replacing joists that rotted because of the lack of drainage, plus put drains under the patio. I think if I was building a patio I would go with one-half inch per foot.

Part2: A retaining wall is not normally used to block water. I assume you mean you may need a wall to transition from the elevation of the neighbor's property to the lower elevation of your property. It is very difficult to say without seeing the actual conditions but a good retaining wall will be expensive. As jasco88 suggested, a good drainage swale should work, even an inlet(s) and pipe might work.