Can I have one FAQ page for my whole store, not just per product?

Yes. The Product FAQs plugin also gives you a store-wide FAQ page at /faq.

1. Open Plugins → Product FAQs.
2. On the Categories tab, add groups such as "Shipping & Delivery".
3. On the Global FAQs tab, add your questions and answers.
4. On the Settings tab, set the Page title, and choose whether to show the FAQ search box and category filter.

Use View /faq page to check it, and add a link to it in your menu.