Let’s assume the playlist I am planning to watch has 10 videos. Today I watched the first 5 videos out of 10. Next day / after some time, how can I continue watching from the 6th video onwards? Currently, it always restarts from the first.
You will need to manually edit the URL. By looking at the URL, you can notice that it's built from 4 parts:
ADDRESS MASK PLAYLIST ID VIDEO ID INDEX NUMBER
For example, to start from 14th video from a given playlist:
https://youtu.be/watch? &list=PLsPUh22kYmNCGaVGuGfKfJl-6RdHiCjo1 &v=fG52mXN-uWI &index=14
playlist ID, video ID and index number can be put in any order you wish. Also, in the first item after address mask you can omit the & character. Shuffle button should be set to off for ultimate chronological playback experience.