He is about to open the door.
What part of speech is "about to" in this sentence? Is it an adjective, or an adverb?
I am really confused, and somewhere I read that it is idiomatic as well.
The word about is an adverb meaning:
very close to doing something
If you omit about, the remaining sentence will be
He is to open the door.
which is a so-called "be to-infinitive" construction which is mainly used to indicate a future event, intention or schedule.
"He is to open the door" doesn't indicate when he will open the door. However, if you add the adverb about, it indicates he will open the door very soon.
Be about to is a more idiomatic expression than be soon to.
Edit: If about is either a preposition or adjective, they cannot be omitted. If you contrast "I was about to call you, but something urgent came up" with "I was to call you, but something urgent came up", you will notice there is no big difference.