Clarification on Gemini API countTokens pricing, rate limits, and counting scope

Gemini API
1

I am using the free tier of the Gemini API.

I would like to clarify the following five points regarding the REST API’s models.countTokens:

  1. Does the statement in the official billing FAQ that “GetTokens API is not billed and does not count toward inference quotas” also apply to the REST API’s models.countTokens?

  2. Can models.countTokens be used for free under the Gemini API free tier?

  3. Do calls to models.countTokens affect the target model’s RPM (requests per minute), TPM (tokens per minute), or RPD (requests per day)?

  4. Are pricing and quota treated the same way for requests containing generateContentRequest?

  5. When generateContentRequest is used, does the returned totalTokens include systemInstruction and the JSON output schema specified in generationConfig.responseFormat.text.schema? If anything is excluded, please let me know.

The model I plan to use is gemini-3.6-flash. I have not set up a Google Cloud billing account.

Thank you in advance for your assistance.