YouTube API to fetch all videos on a channel

You need to look at the YouTube Data API. You will find there documentation about how the API can be accessed. You can also find client libraries.

You could also make the requests yourself. Here is an example URL that retrieves the latest videos from a channel:

https://www.googleapis.com/youtube/v3/search?key={your_key_here}&channelId={channel_id_here}&part=snippet,id&order=date&maxResults=20

After that you will receive a JSON with video ids and details, and you can construct your video URL like this:

http://www.youtube.com/watch?v={video_id_here}