Wouldn't hurt to let your Dr know. If it becomes heavier or turns to red or pink, definitely call them asap.
Very normal! Brown blood is old blood. Drink as much water as possible, then drink some more. You need to keep your uterus hydrated. Rest with your feet up as much as possible, and try not to worry.
Its most probably just implantation bleeding. Had the same with my first one
Some brown discharge is usually normal. Usually only a concern if it's bright red