For 1, pq requires less ink to write than p-p^2. Concise notation is a beautiful thing. Maybe concise means, "Let's use fewer symbols / less ink." But maybe it means, "Let's use fewer distinct symbols." Either is absolutely fine. You can use p-p^2 all over the place, completely ignore q. No problem. This distinction is just aesthetic.
For 2, P(-E < 0 < E) is not equal to c, it's equal to 1. Of course zero is between a positive and a negative number. That is an absolute fact!
The thing that is interesting is that you have a certain confidence that the population value is within some range of the sample value.
For three, of course you don't. If you knew, you would just check the couple, you wouldn't be making an inference. So instead, if you have a couple from group 1, you are deciding whose fault it is with a coin toss, and for group 2, with a weighted coin toss.
LE4dGOLEM: What's a Doug?
Noc: A larval Doogly. They grow the tail and stinger upon reaching adulthood.
Keep waggling your butt brows Brothers.
Or; Is that your eye butthairs?