Is possessing a verb

Answer 1

Yes. It has a few meanings and is not used in the progressive/continuous tenses:

1 to have or own something:

He was charged with possessing a shotgun without a licence.

I'm afraid this is the only suitcase I possess.

The gallery possesses a number of the artist's early works.

Belgium was the first European country to possess a fully-fledged rail network.

2 (formal) to have a particular quality or feature:

I'm afraid he doesn't possess a sense of humour.

He credited her with a maturity she did not possess.

3 [usually passive] (of a feeling, an emotion, etc.) to have a powerful effect on somebody and control the way that they think, behave, etc:

A terrible fear possessed her.

4 (used in negative sentences and questions) to make somebody do something that seems strange or unreasonable:

What possessed him to say such a thing?

Answer 2

Possessing is a verb. It is a verb because a verb means an action word, and when you are possessing something, you are taking control of it, which is performing an action.