Hi,
1. We'll look at adding more width to the left explorer for next version. Note that you can also add a view override of the galleryimage view file via the menu Display>Views and increase the width in the HTML there yourself.
2. Note also that you have the scrollbar at the bottom of the popup to scroll horizontally the left area.
3. Integrating with the Joomla media manager is a good idea and that's something we wanted to look at for a while. However, it has several issues (it requires using the exact same folder as joomla for the images upload for example. Our image selector allows for dynamic folder restrictions. So for vendors creating products on the frontend, there is the possibility to have them only access their own upload folder) and we were also waiting for the new media manager which has been postponed several times (it will apparently be in Joomla 4).