You absolutely can breathe while skydiving! You should be able to take normal breaths in freefall and under the parachute just like you would on the ground. There is plenty of oxygen available to you for the entirety of your jump – in unlimited supply, in fact!
However on your first jumps in an open helmet, you may experience a sensation of air blocking your breathing. It’s totally normal. Just try to look out of the window in a car riding 120 mph! But no worries and no stress. Breath normal and everything will be as on the ground!