So long as it doesn’t explode upon use and you leave the space and return again, yes.
Can I push another hero with my natural tumble? Or only with the skills after that?
Yes you can push another hero with ANY movement. This also includes cards that move you.
The pet Mr Elliot has a symbol on it the I can ignore water. Does it mean that I can ignore currents and whirlspools?
It means you can ignore water currents and whirlpools if you choose.
How do I continue movement after a board element changed my orientation? Example: I may move three spaces in a straight line. A swirl rotates me 90° after my first move. Do I continue movement in the same direction as before (N/S/W/E) or in the new direction (N/S/W/E + 90°)?
The direction of your movement remains unchanged, even though your facing orientation is different. If you started moving North for example you would continue moving North after the whirlpool.
How does “change direction while moving” upgrade work? How does it apply to “jump”?
Normally movement is linear and you cannot change direction when performing any movement. With the change direction upgrade you could you can change direction with each movement point (following rules for that movement skill). For the jump skill: If you have the change directions upgrade you count spaces as you normally would and land one space beyond. As long as you are counting spaces orthogonally you can essentially jump diagonally when you have the change directions upgrade.
Can you natural tumble into a wall/board edge to activate the top face w/o moving
No. Your natural tumble can only be in a direction in which your character is able to actually move. If you cannot tumble naturally in ANY direction, you must respawn at a spawn point (all rules apply) and begin your movement there.
Can i move fewer spaces than my current range allows?
Yes. However you have to move at least one space (in addition to the natural tumble). The only way to NOT move with an activated movement skill is to block the movement against a wall (or board edge). (The Q side is not considered a movement skill.)
Does movement upgrade influence Natural tumble (the initial tumble)?
No. The natural tumble’s range is ALWAYS 1 space
Can you enter a beam power block from any side or just the side with the opening?
You can enter from any side. However, if you are referring to dropping a Crystal onto the power block, for dropping stuff you only need to be adjacent. You cannot however CROSS a beam power block, this means that you must leave a power block in the same direction you entered it.
When moving multiple spaces, do I activate every element on the board as I come across them?
Yes. During each point in movement you must first evaluate any element that is on the board. You may then continue your movement.