Allow me to answer your second question first. It depends on the form. Midnight lycanroc are generally lone wolves (excuse the pun) and will fight anything within its line of sight, including other midnight lycanroc. Midday lycarnroc, on the other hand, are highly loyal, including and especially to other midday lycanroc and rockruff. Consequently, if you have two midday lycanroc in the same room, they will most likely form a pack and get along perfectly, even if they were originally from two completely different packs.
However, to answer your first question, things aren’t quite as simple as that. While the above is true for wild lycanroc, tame lycanroc typically respond to memories instilled in them as rockruff. That is to say, if two rockruff were raised by a single trainer, evolving into two different lycanroc will not make them fight—not normally, anyway. There may be some tension, and if the rockruff didn’t get along before evolving, that will continue after their evolution. But if your rockruff had gotten along quite well before evolution, they will indeed continue to get along, even if one is a midnight and the other is a midday.
Still, always be prepared to moderate any potential bickering over food, water, or sleeping locations. Just in case.
The Pokédex According to Bill 