I have only done this once, in my own backyard, but I am also in the business of aesthetics, so I thought I would chime in. In my situation we went with option #2.
I would not recommend option #3, due to purely aesthetic reasons, unless you would like to keep the fence low all the way down for some reason (light, neighbors wishes, view). Having the gate suddenly jump up by 4' at the end would be quite strange looking, in my opinion.
If you go with option #2 the fence will be high in the back corner, which will allow for taller plants and more landscaping options, and will just look better in general. You get the same effect with option #1, however, it is more of a pain to do all the cuts necessary to slope the bottom, which after a little bit of growth from the landscaping you will never see. It would really be a pointless detail. In my experience, once we got building we were very happy that we had decided against doing that very thing- it's enough work already! And after just a couple months of growth the bottom of the fence was totally obscured anyway.
I wonder if your house is a mid century style? Horizontal fences always look great with this style of house- I also prefer them over vertical for almost everything. I wish I could send you a pic, but I don't live in the house anymore and am renting it out. Anyway, I hope my two cents helps you decide!
What's behind the wooden fence, your back yard? Does the slope get even taller back there? Would you dig out that slope and continue the retaining wall there? You can reasonably build a retaining wall 3-4 feet high without major engineering but when you get to 6-8 feet high it has to retain much more weight (8x as much according to This Old House) and takes more engineering. This may be more than you want to get into.
As Alaska man asked, is the tree next to the sidewalk yours, or is it the city's? What do you plan to do with the brick wall? It would need to be supported or removed also. Would removing the tree or brick wall require city permits or an engineering study? This may also be more trouble than it's worth.
With palm trees and bare dry dirt, I'm guessing you're in a dry area in the south western United States. I'm in the central U.S., where we have thunderstorms 8-10 months out of the year. A good thunderstorm or two would wash that loose dirt slope down against the house and risk toppling the brick wall so I would leave the slope as-is and sod it or put in low ground cover to hold the soil in place. If I used grass I would then have to mow it. I prefer a smooth slope I can just push a lawn mower up, rather than have to pull out a string trimmer for a few square feet of grass on top of a retaining wall. For long-term durability and ease of maintenance, I'd recommend just adding sod or ground cover and leave the slope alone.
Best Answer
I don't know what your goal is, but if it's merely aesthetic (and not for pet or child containment), I'd be inclined to cut a board diagonally. Mark one end at a height equal to the difference in the tops of the two adjacent sections (which looks like about 4 inches). Mark the same at the other end, but from the opposite side. Cut a straight line between marks. This leaves you two nearly-triangular boards.
Install one piece at the bottom of the first section, and the other at the top of the second section. You may need to use additional screws vertically at the narrow end, fastening the last board to the one next to it.
Now you have a nice visual transition without any abrupt jobs. The fence follows the landscape instead of fighting against it, but it retains the nice horizontal orientation in the boards. Adjust grade slightly to account for any remaining gap at the bottom, or add a little additional mulch.