First screenshot - top door is unlocked by popping jumping clouds in the background, how to open the bottom one - no clue.
As for the door on the second screenshot - i think it's about hitting the furthest sphere, but it exceeds sling's maximum range(?). Maybe after some moment we get a tool to move the slings/spheres, but for now i have no clue how to reach it.
Second screenshot, in the slingshot room there's a removable brick with another slingshot that allows you to hit the previously unreachable sphere.
If anyone knows how to open the the second door in the first screenshot I would be delighted, I've been stuck on it for ages.
I've tried checking every room and wall in this floor, tried to check for secret passage in the two room above and found nothing, I'm getting quite close from a nervous breakdown here