Unknown Trees... Dry Stone Wall... Can I grow a Beech hedge?

[peatff]

I wouldn't try to go higher with the dry stone wall, gravity is a cruel mistress and you will be forever replacing bits.

[growforest]

If you want to keep your repaired wall in good condition, best not to plant anything behind it - will compromise the wall in the end. Repair the wall and add a larch fence behind. Feel free to pm if you want a competitive price for walling. I'm guessing Oxfordshire from the stone.