First the premise:

- We know that movement points from special actions (e.g. Vader's Finest or Hit and Run) behave differently than movement points in general. They don't go in your MP piggy bank as they usually would during your activation and instead have to be spent immediately (RRG p. 3).
- That you cannot end you action in an illegal space. For instance you could not use the two movement points from Vader's Finest to move into a space with another figure, even if you still have other movement points in your regular piggy bank from other sources (like having performed a move earlier during your activation that would allow you to move on. This is because of your action having to be completed fully and not specifically about movement points.

Then the question(s):

But what it if you are not looking to move, but you want to spend the movement points on something else. For instance Raining Freight on the Nal Hutta Swamp skirmish map. If I get 3 movement points from Hit 'n' Run, could I then pick two crates, in case I had a spare movement point in my 'piggy bank' to add to that from the special action?

And what about moving into difficult terrain using the last movement point from the special action + one from the 'piggy bank'? I'm moving into a space I can legally stay in, unlike if I were moving on top of another figure, which is what I presume is what usually prevents the blending of movement points from the special action and the bank.

Spending movement points for other effects depends on the wording of the mission rule. i.e. whether it includes "during your activation" or not. For example if it is "while adjacent to X" without "during your activation", it can be performed if receiving movement points during someone else's activation and also when receiving movement points from a special action. (Spending mps from both the special action and the mp pool would probably be allowed in this case.)

You can not move by spending movement points from the movement point pool during a special action, because moving is a "during an activation" ability. You need to spend the movement points from the special action before being able to spend some from the movement point pool. (You already mentioned why by referring to Vader's Finest / Overrun ruling.)