I've never closed up but if I were....
Personal conversation with a letter in hand. Would have a brief conversation with parent at pick up or drop off time (whichever is less busy) and hand them the letter to read at home in greater detail.
I'd likely give 3 month's notice if I could. If it was due to an emergency than as much notice as possible but life happens and parents in hdc's take the risk of potentially not having daycare in a very short notice.
Again, depends on the situation. If it was for an emergency than yes a hard close date. If I was able, I would accommodate for as long as possible if it didn't disrupt my future plans.
I'd give the exact reason most likely. I'm pretty open and honest.