Jumping under block

Use the 'When entity collides in the block' function. You may have to make your block model slightly smaller at the bottom (change your bounding box to start at Y = 1, instead of Y = 0).

To certify the player being below the block, build this in the procedure:
'If (y position of (Event/Target Entity)) < (y)'

do: (put the rest of your procedure here).

is the 'when entity collides in the block' function based on the model?

yes

"is entity inside a solid wall" inside the entity data section

I think the only way to determine if any entity is in specific block is through the blocks "when entity collides in block trigger"