Up to the DM

This is about it. As far as I am aware, the rules do not specify how the creature will occupy the space after being transformed. In particular, there are few specifications on how to play using miniatures/grid on the core books.

For the adjudication, as Rykara mentions in the related answer

the grid space of a map does not represent the actual space a creature occupies, it represents the space that creature controls

so, there are a few things to consider: First, enlarging a creature might not require it to actually occupy the space suggested for a larger creature, which is also backed by the DMG (p. 251):

For example, you might use a miniature that has a Large base to represent a Huge giant. That giant takes up less space on the battlefield than its size suggests, but it is still Huge for the purposes of rules like grappling.

Second, if you are using the optional "facing" rules (DMG, p. 252), it would make sense that the space the creature controls is defined by the way the creature was facing.

Finally, for your scenarios where the creature is, for example, surrounded, it would make sense that the creatures are pushed back, if the creature growing is in fact enlarging enough for it to occupy other spaces. Also, on your quote, note that

Whether a creature is a friend or an enemy, you can't willingly end your move in its space.

This means creatures can occupy the same space, they just can't do it willingly (in particular, they can't willingly enter other creature's space by moving and stay there). Thus another possible adjudication in this case (surrounded creature) is simply allowing them to occupy the same space and, in the monsters' turns, they are forced to move out of the space (as they can't willingly stay there). (The character doesn't have an option unless the monsters are Small or smaller, since he can't move through the monsters).

From my experience¹, ultimately none of this should have a relevant impact in the game, so you can adjudicate as you want and it should be fine if this situation shows up in an actual game.

¹ Just for reference I have played lots of wizards with Polymorphs and Enlarge/Reduces in online tables (with grid/miniatures) and I can't recall one time when the occupied spaces would have been game-changing. The DM/I just increased the token's size as we saw fit and moved on.

The rule requires that you not willingly end your turn in another creature's space. Sometimes you will be prevented from taking actions in order to make sure the rule holds true.

The DM always has jurisdiction over edge-cases like this and will often make rulings on consequences and benefits, so although I speak from the perspective of being a DM myself, my own interpretations will not always hold true.

Willing and unwilling do not have mechanical definitions, but here's how I would rule them for practical use.

Unwilling:

• Effects that have a risk but not a guarantee of forcing your turn to end in that space

Willing:

• Effects that guarantee you will end your turn in that space which are not hidden from player knowledge
• Effects coordinated with a party member to place you in a space.

Regarding your examples:

1. You must not willingly spend movement to end in the creature's space. In the case that they're forced unwillingly into the space after/before movement, such as by a grapple, RAW does not require action economy (misty step, breaking grapples, dashes, etc) to be spent on vacating the space.

   Sidenote to 1: The rules are unclear whether a player may receive their once-per-turn movement and not spend it to remain occupying the space, but this is clearly against the spirit of the rule. If a player has movement, I believe it should be spent to vacate the space. I also believe that actions a player controls (such as misty step and falling from above) should not cause the space to be occupied, but I would rule these on a case-by-case basis.

2. This is a tougher one to rule on. RAW you can attempt to spend movement to pass through the space and unwillingly have your movement reduced to 0 in that space. The creature must be friendly or your size class has to permit movement through it's space (size class overrules this general rule).

3. This would likely require a rollback. You willingly spent movement and then realized it was movement you couldn't use. You broke a rule, the DM will likely undo the action that broke it or offer you an alternative (such as taking disadvantage).