Unless otherwise stated in your deeds you do not have to fence your land. You do however have to make sure your animals are adequately housed and cannot escape to get hurt or do damage.
In some instances the height of a fence at the front of the property cannot be higher than 1mt high or may have a condition of planning making the area open plan so no fences can be built. Check with planning what the requirements are for your area.
If the fence is yours, on your land your neighbour cannot attach anything to it, paint it or stain it or grow anything up it unless you give him permission. He cannot make you replace it or repair it and as long as it doesn't fall into his land and damage his property you can leave it to rot if you like.
If he has weekened it by attaching things to it you could ask for a contribution to remedial works but he doesn't have to. You could also tell him not to use your fence as a prop for his stuff. That may make him realise he is damaging it.
He can if he wishes put up his own fence tight up to yours, but again cannot attach it to your fence. This, however, is fraught with difficulty later when someone sells and decides to take one of the fences down.