Get new post/reply/comment within a specific time interval

There are APIs for listing these types of entities, but they may not be exactly what you're requesting.

For forum threads, dates can be passed.

For forum replies, they cannot, but you can still get all replies to a thread and review the replies' dates.

Likewise, comments can be listed, but again not with date offsets directly in the query.

Are you just trying to get a list of all activity on the site within a date window? If so, the activity story service may be a better match for you. This API is the same API which powers the activity story stream. It can be filtered by date and type of story. However, users can opt out of generating stories for their actions - so it's not guaranteed to contain everything.

See "Activity Tracking" here:

Thanks Ben Tiedt  for the above information. Our setting is "Always On - Hidden" for all types.

We created two test forum threads and also replied to these threads. When fetching the activityStory list using API core_v2_activityStory.List we are getting the forum threads but not the replies to it. Is there anyway we can fetch the replies to these threads?

Replies are not represented by the activity stream API. You would need to identify that the story represents a forum thread and then load the replies from the forum replies API (this is how the activity story stream widget is implemented).