Does the FAQ section in the page builder add FAQ markup for Google?

Only if you switch it on. In the FAQ or FAQ Numbered section, on the Content tab:

1. Under Questions, click + Add question and fill in Question and Answer for each one.
2. Tick Add FAQ Schema for Search Engines.
3. Click Save.

The markup is built only from questions you added yourself. The sample questions a new section shows are never sent. Google decides whether to show them in results.

Other options on the same tab: View (Accordion — one open at a time, Accordion in columns or Always open), Open the First Question and Number the Questions.

Tick the schema box on only one section per page.