1. Use of the API itself is actually entirely free. The API is built such that developers can create apps that any kind of Dropbox account can link to. It is only if the owners of any individual (or group of) accounts want to upgrade is there cost involved. You can see more information on pricing and plans here: https://www.dropbox.com/plans
2. The Dropbox API doesn't have a limit on the number of devices that can access the API for any particular app/user/team.
3. The Dropbox API does have a general rate limiting system, but note that not all 429s and 503s indicate explicit rate limiting. In any case that you get a 429 or 503 the best practice is to retry the request, respecting the Retry-After header if given in the response, or using an exponential back-off, if not.
For example, if you're making multiple changes at the same time in the same account or shared folder, you can run in to a 'too_many_write_operations' error, which is "lock contention". That's not explicit rate limiting, but rather a result of how Dropbox works on the backend. This is a technical inability to make a modification in the account or shared folder at the time of the API call. This error indicates that there was simultaneous activity in the account or shared folder preventing your app from making the state-modifying call (e.g., adding, editing, moving, or deleting files/folders) it is attempting. The simultaneous activity could be coming from your app itself, or elsewhere, e.g., from the user's desktop client. It can come from the same user, or another member of a shared folder. You can find more information about lock contention here: https://www.dropbox.com/developers/reference/data-ingress-guide
4. We have a Getting Started guide here that may be helpful to show the overall process of developing with the Dropbox API: https://www.dropbox.com/developers/reference/getting-started . There's also a number of other guides and resources linked here: https://www.dropbox.com/developers/reference
