Thanks for contacting us here about this extension.
1) Are these extensions front-end accessible for managing?
Yes, you can access image management in frontend.
2) What is the permission structure for such front-end management like on these extensions?
Our droppics doesn't have level for access. If users have permission to access backend site on frontend, they can see all galleries and images.
3) What is the compatibility with Joomla 4 like? That is do they work currently with the beta version of Joomla 4 or does that mean a wait for the stable version and if so how long after the stable version is released are compatibility expected to be resolved?
We will check the compatibility with the latest version of Joomla. If you encounter any issues with Joomla 4.x beta, our dev will fix for you.
Hope it helps!