This is called bender board. Typically made of Redwood for rot resistance.
It is used as edging for gardening and lawns, forms for concrete walkways and base material for making lattice.
Available on the US West Coast either direct from Redwood products mills or from Lowe's or Home Depot in thicknesses from 1/4" to 3/8"
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!
Best Answer
The hanger you have pictured is not correct for the panel you have pictured as the 2x4 is not oriented correctly for them.
If you are not comfortable using just deck screws you could put an L bracket on the bottom of the panel to carry the weight of it and use a 1/4" lag bolt or carriage bolt at the top for lateral or shear strength