In Texas, if he is on your land, and the land is not posted, it is not trespassing until you ask him to leave and he refuses. Then it becomes criminal trespassing. If the land is posted (and there are rules governing how it is to be posted), then it is criminal trespassing the moment he steps on it.
If I were you, I would try very hard to come to some terms with this guy...jerk or not. There are few things that are more unsettling than having a neighbor on bad terms with you, especially when you own animals. Try hard to make some peace....give him a couple of dozen eggs every now and then.....if it works, you can have peace of mind. If not, you will at least know that you tried to make peace. Remember, a LOT of people don't care for chickens one little bit, and from their perspective, a rooster crowing is a nuisance they have to be subjected to, in their own home, on their own property....all because YOU want to keep a few chickens.
On the subject of your livestock in his yard...you'd have to check your local ordinances, but if it were a cow or horse that wandered onto his property I don't think he would rightfully be able to kill it; especially knowing it was yours, but I don't know if this extends to chickens, dogs, cats, etc. especially when 1.) he perceives them as a nuisance and 2.) it happens repeatedly because you have made no effort to correct the problem.
I hope I'm not being hard on you...I love chickens and enjoy hearing a rooster crow...but I have been through an issue with a crazy neighbor, too...........we had been okay neighbors for years; just waving and making occasional small talk. One weekend I see him and his family packed up in an SUV pulling a trailer, leaving the house, and I notice he didn't take his dog, who was still in the yard. A day or two later, I notice he was still gone and asked another neighbor if he knew if the dog had food and water and they told me that from their yard they could see he had food and water, so I quit worrying about it. Two days later, this guy is banging with his fists on my front door....telling me that I had been trying to STEAL his dog (I guess the other neighbors told him I had asked about it) and that if I ever set foot on his property he would call the law, and if my dog ever went in his yard he would shoot and kill it...he was violent...cursing and screaming. I tried to explain to him that I was just trying to check on his dog and make sure it had water, but he wouldn't have it. I finally had to stick a 12 gauge shotgun in his face to get him off my porch and property, and he moved a few months later, but it was very unsettling, especially when I was away from home, to know this guy next door had an axe to grind. I would hate to see you in that same position if there is any way to avoid it.
DD
You may be able to find your local ordinances here :
https://www.backyardchickens.com/laws/search.php