Probably the most economical approach for the retaining wall would be salvage railroad ties. They can last a long time even a sub-grade.

Your privacy fence should be anchored on the inside of the retaining wall mostly because you would have to take the post to the bottom of the wall on the outside making the material cost more. If you have running water at times you would also not have to worry about it getting washed away.

I would make a center drain with a slight slope like a shower drain. I would take this and empty into the easement area unless there are codes that prevent this.

I would pave the whole area and use astroturf instead if grass. I know if mine was in an area like this it would be dug up in no time.

The housing area is something you can decide on based on cost, and how much you are ready to spend.