You'll find your answer right here.
Should i put on sunscreen before or after my primer? I have very fair skin and I would like to keep it that way
I concur with the answer from the website Rooster Cogburn linked to from personal experience. You should put on skin product (moisturizer, sunscreen, whitening cream, etc.) before any kind of makeup (primer, foundation, BB cream, etc.). Makeup prevents skin products from being absorbed by your skin and thus reduces the effectiveness of your skin product.
Yes you should !
Forget the sunscreen. Buy a parasol. You'll start a new trend.