Not a great picture, but it looks to me the cable leaves the shifter at an angle, this will inhibit the movement of the inner cable and would contribute to overall stiffness that you describe. You'll need to release the cable at the derailleur end and re-seat the cable outer before re-tightening the cable at the derailleur end. If this funny angle is a result of the cable being too short, you'll need a longer piece of cable outer and a new inner cable too. No clues here about the brake though. You'll need to adjust the derailleur after releasing it, so if you are not a DIY'er, take it to a proper bike shop.