Publishing a page and telling anyone about it are two different jobs, and the second one is usually the one that slips.
Connect X and the announcement can happen in the same flow as the publish.
Embedding a timeline through a widget hands a third party a script on every page of your site. Reading it through the connector keeps that off the page.
To post, yes. Reading works on the free tier.
The app-only Bearer Token from the developer portal.
Yes. Connectors are part of the plan; there is no separate integration fee.