Which entity does represent it? How to get data from it using WEB API? I do not find any information about how to fetch data from 'Timeline' window on account and contact entities. Is it possible to query all necessary info using /api/data?
Timeline is not an entity and not expose via web api endpoint. It's a custom PCF control (maybe) and all about a placeholder for showing all activities, Notes, Posts for that particular record in chronological order. Btw, Timeline can be added to Dashboard also. Read more
You can pull all the activities, Notes (annotation), Post feed & display in the same fashion if you build a portal separately.