category of phrases

Only the third one is even remotely grammatically correct.

It sounded weird to me too, but it is from a sample exam that I have .
However ignore the 3 one

I didn't think that any of them resembled English--but what do i know, i've only spoken English for a little over 60 years.

Jes, a phrase doesn't have to be. For instance

Adam having been described as "unbelievably fast," his dad was reported to remark, "Unbelievably fast Adam's first encounter with problems nonetheless slowed him down considerably"

The purist however might insist on a hyphen in the compound mod describing Adam

Then Cric is it not a noun phrase around "encounter", or maybe subject. There are by actual count 1,753 other perfectly grammatical ways the phrase might be used. For instance: Unbelievably, fast Adam's first encounter with problems occurred as he stepped out of his ship onto the surface of Mars

That number increases to 4,502 if you allow punctuation, eg, It was unbelievably fast, Adam's first encounter with problems