How do I buy an archive service?

It seems that there is no button to purchase this service?

Thank you for your message. To purchase just Archive Data you would need to visit this page once logged in:

From there, you can select the Plan you want to subscribe to and add the Archive Data Add-On.

Hope this helps!

Are there some limitation on requests for Archive mode?

They are subject to the same request limits as the tiers. For example, if you remain on Core and just add Archive Data, you would be subject to the 100,000 requests/day.