Is youtube data api totally free

Yes it is, but some restrictions like limit you can use only 100000 units per day. and 3000 per second per 100 user per day. For more quotas you have to apply for it. You can apply key or oauth id at HERE. Hope it will help you.

Yes, using the YouTube API does not incur any monetary cost for the entity calling the API. If you go over your quota an 403 Error will be returned by the API.

Links:
YouTube API Quota Details
YouTube Quota Calculator

Google already provides a Python client for all of its APIs, including YouTube, which handles authentication, forming and making the API request as well as some datatype translation (i.e. JSON to dictionary, etc.). (link)