How to place nuts on top of the cake so that they stay symmetrically?
Many cakes have the nuts applied after cooking, held down with some sort of glaze. That will keep them where you put them so long as the top is reasonably flat. It will also prevent them burning, as nuts are often used to top cakes that cook for quite a long time. 

If nuts are going to be baked on top of a cake, I'd expect to need a dense recipe that doesn't rise much, as the rising will be what causes them to move. The classic Dundee cake (which uses almonds) is such a cake. 

This Dundee cake recipe takes an interesting approach: the nuts are added when the cake is part way through cooking. You couldn't do this with a sponge cake, or it would sink, but a more robust cake, cooked slowly, apparently works.