Hi,
A woman who spent eight days trapped in a wrecked vehicle has severe injuries, but her brain function is normal, and she can move her arms and legs,
Iy's not necessary.
'And' is sufficient to join these two short main clauses. If either of them were long and complex, a comma might be useful to make the sentence easier to follow.
You also don't need the comma after 'legs'. A period would be preferable.![Smile [:)]](/emoticons/emotion-1.gif)
Best wishes, Clive