That is the very reason why custom entropy is not proposed in the GUI.
The second issue with custom entropy and the multiplication is real; thank you for pointing it out.
I too believe that the custom entropy option should be removed from the code.
Actually, I did remove it 6 months ago:
https://github.com/spesmilo/electrum/commit/e0c38b31b40b42138527e9fd3f4bad78e0b12802
and I later reverted that commit because users were complaining.
Yes, but since most people will just type there their birthdate, their spouses birthdate, their kids birthdate, their marriage date, their phone number ....whatever, that could be a long concatenated string of many numbers, that might look like strong, but it actually has 0 entropy since all of the dates are public if associated with the user.
Look I am not crypto expert but I have researched some basic cryptographic concepts as a part of my due diligence when investing in cryptocurrencies, and I have analyzed the electrum wallet to the best of my knowledge, and this code struck me as odd.
So I am glad that I helped you fix this issue.