 Re: picking up
Yes - it's a verb plus adverb, so a phrasal verb. Here it's used intransitively, but the full meaning, as you say, would be :
She's not picking up the phone.
She's not picking the phone up.
The fact that
a) it can be used intransitively
and
b) when it's transitive the verb and particle are separable
shows that the particle is an adverb (rather then a preposition) and it's therefore a phrasal verb rather than a prepositional verb |