Zombies are meant as exactly how you experience them. HOLY FUCK, THIS IS NOT WHAT WE EXPECTED!!!!
Chance for Zombies is about 5% for several missions, just to give you a little something to be worried about.
Concerning bows, I only consider the poison arrow variant worth using. There really is a huge difference. Normal arrows roll damage, and then roll again for health damage, which effectively halves the damage again. In contrast poison arrows have the two dice roll like sniper rifles and plasma, so are very consistent.
The thing about spartans is, they have the sniper/spotter behavoior, which you might not know about. Basically, if one of your units is spotted, they have maphack on that unit and know where it is for a few turns. And knowing where it is, all sniper enabled units can target it, even if they can't see it. Spartans have a lot of sniper enabled units. This then results in lots of grenades beeing thrown, as a regular shot is likely blocked by terrain. The only thing that helps is stand in places where they can not throw a grenade. The AI can only target the tile your gal is standing on, so it is sufficient that tile cannot be thrown at.