About sharedInbox, maybe this thread has some clarification.
If not please add it to the guide :
Introduction to ActivityPub
About
I’m having trouble with this part. Don’t I need to bring this data into my local data model, so that it can be queried and presented to my users?
Yes but this is only specific to your app. We talked about it in the journalism session at 36c3 and everybody handles this different apart from the “id”. For example some only store hashtags, others store a special search index and a link index plus from/to relations.