Is there a Vimeo API for videos, profiles and collections?

Yes. Social Fetch has 31 Vimeo routes under /v1/vimeo: video, embed, captions, comments, credits and likers; user profiles and their videos, likes, appearances, showcases, channels, groups, followers and following; channel, group and showcase records with their videos, subscribers or members; video, user, channel and group search; categories, tag videos and On Demand titles; and a browse route. Authenticate with your Social Fetch API key in x-api-key.