Is the business analyst part of the Developers team and has to participate in the Daily Scrum meeting?
Some Scrum teams have a business analyst, and it's unclear for me where that role fits. Is he or she part of the PO "team" or is the BA considered a Developer. I wonder if the BA has to "participate" in Daily Scrum meetings, or the BA can just "attend" the daily.
Is their work necessary for a Done increment to be developed and made usable?
There is no "PO Team". Specifically, the Scrum Guide says: "The Product Owner is one person, not a committee." However, that doesn't mean that there can't be a small team supporting the Product Owner. Even so, the Product Owner is ultimately accountable for managing the Product Backlog.
The Developers are everyone on the team "that are committed to creating any aspect of a usable Increment each Sprint".
If the BA is working toward creating the usable Increment, then they would be considered a Developer. However, if they are supporting the Product Owner, they could be doing so outside the context of the Scrum Team. Unfortunately, I've seen little guidance about incorporating people supporting the Product Owner in the Scrum Guide or other sources. It could be a matter of trial-and-error to figure out the best interactions in your particular context.