If the wall is in a poor state of repair then you would be liable if part of it fell & caused damage or injury - check your household policy to see if you are covered.
Take down the wall to prevent accidents.
If you want a hedge it will take time to grow. The faster it grows in the beginning the more maintenance you will have to do in the coming years - cutting & removing rubbish.
I suggest a basic fence, just posts & wire. This can be used to grow plants up or train a hedge. You could put in pannels instead of the wire, gradually, until you fence the whole thing but you'll have to treat the wood regularly. Or build brick piers & fill in with fence pannels. In time you could brick in the gaps until the wall is back.
If you take a bricklaying course you could do it yourself but by the time you've messed about I would just invest in having the wall repaired/ rebuilt. You might be able to save some money on the job by being the 'brickies' labourer.