1 - Assessment is the action to verify the token sent by reCAPTCHA and assess the risk. So only the token verification will be calculated (whatever with a BACKEND or with WAF)
https://cloud.google.com/recaptcha/docs/implementation-workflow
2 - The free 10,000 assessments are per organization. The limit aggregates use across all accounts and all sites.
https://cloud.google.com/recaptcha/docs/compare-tiers