Dead birds are just found by happenstance on the ground. Usually foxes or wolves kill some of the nearby chickens or foul and leave the corpse for you to scavenge from.
So, the number of handbaskets . . . it all depends on your map and how limited your resources and time might be once you find cattails. Cattails can be very scarce in some areas and you really want to ration it out across each day in order to make sure that you don't run out during moments when you need it the most. If you have lots, no problem, make as much as you want (within reason lol).
Yes, the haybales keep monsters and animals from entering. I was skeptical of this at first, but yeah, it works really well.