Why did Gandalf save Faramir?

[Raynor]

did he really enter the halls of Mandos?

No, because he went "out of thought and time".

Originally Posted by Letter #156

Gandalf really 'died', and was changed... He was sent by a mere prudent plan of the angelic Valar or governors; but Authority had taken up this plan and enlarged it, at the moment of its failure. 'Naked I was sent back – for a brief time, until my task is done'. Sent back by whom, and whence? Not by the 'gods' whose business is only with this embodied world and its time; for he passed 'out of thought and time'.