When rescuing my friendlies, what factors apply nowadays?

Say Storm and Wolverine are up against Wrecker. Wolvie is adjacent to Wrecker, Storm is adjacent to Wolvie but not Wrecker. Can she whisk Wolvie away and no break away required on Wolvie's part?
I presume her adjacency is still a must.

Is this rule the same for & ?

Could a transporter or vehicle move, grab and escape or is adjacency still a must?

It works the same way as it always did. Since Storm is not adjacent to an enemy, she does not need to break away. Since Wolverine is placed by Storm's Carry ability, he does not need to break away. (OK, the place bit was added later, but mechanically it has always worked this way)
The Carry ability works the same way for pretty much anyone who has it, with reservation for special powers or traits of course.

The Carry ability says the character must start adjacent to the friendly.

No breakaway is needed if the carrier is not adjacent to an opposing character.

so this part won't work. You have to start adjacent to the character.

That pretty much nails it, thank you all.