No,
1. No - this would kill your performance
2. Depends - I think with 100.000 images you should read this howto first:
http://www.tinywebgallery.com/en/faq.php#h45 There you see where caching is done!
3. Data is stored in xml. There is nothing you can do. In my opinion the 100.000 images make the session so big.
"If you have really many images and the 1st start of the gallery takes very long most likely this is the counting of all images for the "number of images" counter. This counting is cached but the 1st call could timeout if your server settings are to low. You should set $show_counter_in_jstree=false and $show_number_of_pic=false; then. The counter is then not shown anymore. " Is the important one for you. If you do this settings then the whole directory structure is not crawled anymore but only the ones needed for the current page. Do this setting first and check the session size.
4. Ask your hoster. If you don't have access you can e.g. change the session save path to a directory you can access and cleanup if needed.
1 user? I'm talking about visitors. one visitor generate one session! If you don't have so many visitors than the cleanup of sessions do not work properly. This has to be checked as well.
Best, Michael