Is it allowed to record videos from a website with a screen recorder?
Does the website notice that you are doing this?
It is not about films like those from Netflix & Co, but simple videos, e.g. Tutorials, which can be seen e.g. On a website (also for a fee with subscription).
Recording for private purposes is ok
Ok, but does the website notice that you are doing this?
I do not think so.
The website does not notice that you are filming your screen.