Regards him taking your friends fence down,. he has no right, why are they not taking this up with the police.
Boundaries can be a sauce of great problems. Usually they are defined in the deeds both for the house and the field. Sometimes, with the passage of time, these can become blured. At some point in time the garden would have been split from the field, and the boundary line should have been registered in the deeds and the land registry, maybe with conditions placed regarding the actual fence. It could be that the farmer has to erect and maintain a stock proof fence, or it could fall to the house owner, depends what was written at the time. of course he has a liability to fence to keep stock on his side, but until the deeds are read, the conditions are not known. A check with land registry on line may clarify this. But, if he owns the fence and the responsibility for the up keep and the boundary line its self is his, then he can remove the original fence and replace it with another, the height and style being his choice. Providing it keeps his animals in his field there should be no problem for him. It would then be down to the house owner to fence their garden to keep their dogs in. very often it is not as cut and dried as that, and can be a quite expensive and lengthy proceedure using solicitors to actually clarify whose boundary fence it actually is, and where it lies (removal and re erection of fences can move the line over, a verbal agreement with a previous occupier could mean the fence is not actually owned by who it states in the deeds, the farmer could have put a fence up behind a hedge or fence that belonged to the garden, then the householder removed his, leaving the farmers fence. boundaries can get confused and messy).
Footpaths are always a matter of concern, for the landowner and footpath users. The land, footpath or not, is needed to be used for the farmer be that crop or stock, and provided he follows the law as to what goes in there, it is up to him how he farms it. The trouble comes when foot followers abuse their right to follow the path. The path is there to get from A to B, that has been the whole point of it from when farmworkers walked them to get to work, or the mill, or whatever. They are not a picnic area, they are a means to get from point A to B. the whole field is not a playground for children or dogs, and all gates should be shut and dog mess collected, the same as if you were on a road. It is manners, you are walking on someones elses ground and should show the same respect as you would to anyone elses property, say at a show, game fair, or whatever, and clean up after you of any litter. How many times have you all seen the field with a footpath being used to run dogs, with balls being thrown and dogs chasing everywhere. This is what can annoy a landowner, and it is not what the path is there for, it should be followed with the dog under control. How would you feel if someone came up your drive, round the back, left gates open, let their dog poo on your lawn, then walked off? When leaving the footpath, and not cleaning up after your dog when on it, you are doing exactly the same thing. Trespassing, which you wouldn't like any more than the farmer would.
It is the people who think they have a right to do what they like in fields, with or without footpaths, that quite rightly annoy farmers. If you owned horses and had a horse injured by a chasing dog, or spooked by balls or children playing shouting and screaming as they do, or any other farm animal that was distressed by the like, then you wouldn't be to happy and this is sadly when heated words can be passed.
The chap the OP refers to. he may just be a 'mad head' or it could well be that he has encountered serious problems with his animals in the past due to walkers and wants to come down with a heavy hand before any problems arise. None of us know the full story or reasons behind his actions. If everyone followed the country code, gave respect to the landowner who's land is being walked on, then maybe there wouldn't be the problems. Can only say, owning land with a footpath would be a nightmare and I do feel sorry for those that have them, especially now the weather is improving. It was a bad enough experience when we lived next to a footpath. I also feel sympathy for those responsible walkers that do use the paths for the use they were intended, as usual being 'lumped in' with the selfish idiots and abused by the landowner.
As to shooting dogs on land, I am sure someone better at finding things than I can, could look up the legality of shooting near a footpath, but I do believe there is a distance where a gun is not to be fired near a road or ROW, so the dog would have to be well into the field to be shot and out of control?