Can I rename the Request a Quote button and hide the price in the quote popup?

Yes. Both are in the Request for Quote settings.

1. Go to Orders → Quote Requests and click Settings.
2. In Button label, type the new text, for example Get Bulk Pricing. The popup heading uses the same text.
3. Untick Show price in popup to hide the product price in the popup.
4. Click Save settings.

To show the button only on some products, set Button visibility to Selected products only in the same panel. Then open each of those products, tick Enable “Request a Quote” (selective mode) in the Status box and click Save. Make sure Enable Request a Quote stays ticked, or the button won't appear at all.