To view your allowed quota please create a project in the Google APIs Console. In the “Service” tab, the default quota allowed for each service is indicated.
Currently for the Drive API it reads “Courtesy limit: 1,000,000,000 queries/day”. It’s a per app quota.
After you’ve enabled the Drive API you can also set a per user rate limit (by default 1000 req per 100 sec) to prevent one user from depleting your app’s quota. That’s available in the “Quotas” tab.
There is also a link to request more quota in the “Quotas” tab in case you need more than the default 10M req/day such requests will go through a (light) manual review process.
Also files have per-files playback limit which depends on many factors (Is the file shared publicly or just to your domain/users? Is it a video? An audio file? etc…). These rules are not disclosed at this point unfortunately but for instance a publicly shared video can’t be viewed by millions of anonymous sessions per day (use Youtube for that). Nor can an image be used on a high traffic website. Google Drive cannot be used as a Web scale CDN, it is scaled for personal content sharing (you share files with friends/work group/company).