Can we consider a widget as a good re-presenter of latest activities, e.g: Latest News, Latest Announcements, Latest Offers..and so on ? And Does it make sense to put a widget among the content? I think it should be located in the side bar.
A "widget" can be seen as more of an implementation methodology than just a UI component or concept. Whether to use widgets or some other means depends greatly on the framework or platform. Nonetheless, I think that the "Latest ..." you describe are good candidates to be implemented as widgets.
If it's reasonable to have just the latest news or latest announcements as the main content, the question is kind of meaningless. I'd say that if the latest of X has no meaning when mixed within the content, the widgets should stay separately in the sidebar or at the bottom of the page.
And one example of the reverse; if your content has some entities (e.g. persons or organizations) you could put a small (perhaps expanding) widget in direct proximition of the entity to give shortcuts to recent news or activities related to the person or organization.