1: Yes, imo it is way more realistic than a horse getting headshotted by an arrow and being ok, its on the same level as you whistling to a horse and it sprouting out of nowhere, its something that can be easily overlooked for the sake of convenience, while immortality imo isn't
2: In RDR nobody ever complained about the horse AI, CDPR could very well choose to go that way instead of doing it skyrim style, plus it adds to the whole atmosphere if your horse dies and you are stranded, as long as you get all your item stash(the actual inventory wll be on geralt) back as soon as you get a new horse
To me, the best solution would be that your horse is vulnerable to attacks, but cannot. On hit he should flail and wave, possibly unsaddling you, or fall to the ground.
This way the battles would be more exciting and risky and you wouldn't lose your items.