Build garden fence on or beside uneven concrete base?

That's the problem: the neighbors are "specifically pleasant" and have 3 children without manners. The hedge plants wouldn't survive 2 months without being trampled. Therefore, the fence must come first. Fence on the neighbor's property will not work.

Build the fence of your choice on the base, make sure it is straight at the top and grind off a few centimeters here and there at the bottom. This way you get a straight fence on the uneven base. The subtle individuality will give it a good character.

How big are the height differences? I don’t mean the general slope with the 40cm but if you lay a 3m batten (better yet a straight edge) on the wall. How big is the maximum gap between the batten and the wall?
Up to 2cm could be compensated with decking boards, which should be installed with a slight slope anyway so that the water can run off.
Regarding the hedge, you could first plant a hedge on your own side, as you really want it, and place pots with young [Robinias] on the base (best to collect wild ones somewhere along the railway embankment). [Robinias] are super tough and undemanding, grow very quickly at first, and young [Robinias] have long sharp thorns. Have fun kids... hehe...
A [Robinia] at our place grew two meters tall in the gravel within two years. We’ve now planted it out and put it in a pot, my wife wants to reward its toughness.
She didn’t think it would really survive though, because we had to cut some roots.
Now, a few weeks later, it’s even blooming...