Can I validate my whole site with this tool?

Not in a single click, the validator takes one JSON-LD snippet at a time. But you don’t need to validate every page; you need to validate every template.

For most Magento stores, that means 6-10 snippets:

1. One Product JSON-LD from a Simple PDP
2. One from a Configurable PDP
3. One from a Bundle PDP (if you use them)
4. One Category JSON-LD (often empty, which is its own problem, the validator catches that too)
5. One Article JSON-LD from your blog
6. One Article from a CMS service page
7. One FAQPage from a CMS / pillar page
8. One Organization (homepage)
9. One BreadcrumbList from any non-home page
10. One LocalBusiness (if applicable)

That covers ~95% of your URL surface. If any of those fail validation, every page of that template fails. Fix the template once; fix the whole site at once.

For a full automated crawl (which is what big agencies sell as a $5k schema audit), I do it manually as part of the full-site audit service, crawl up to 500 URLs, validate each JSON-LD, deduplicate by template, ship a per-template fix list. 48 hours, fixed price.