The picture is rather dark, so detail isn't easy to pick out, but it looks to me as if you'll need advice from your local council as to what you can and can't do. That slope, which seems to be just soil, too dark to tell properly, looks pretty steep - hopefully, some kind of retention has been put in place to prevent erosion, and if it hasn't, then a landscape architect should be consulted.

Yes. Looks as though it needs terracing. If you are not allowed to alter the fence you can always plant some tall shrubs behind it. I hope the foundations of the house are secure, its very near the edge of the slope. You definitely need expert advice as Bamboo says.

you cant have the fence higher as rules is rules . your going to need steps bye the looks of it so maybe do steps that are living too go with the ones you walk on . you could have a nice water feacture too .

I would plant Delphiniums all along that wall, if the soil
is rich enough. Make a good colour feature.