You will be able to select between the drop-down (current) method and "all on one page" method in the next release of the user module - that's coming soon.
Looking at this some more, my suspicion is that you have a {jrCore_list} call either in your header.tpl or footer.tpl that is relying on a variable being set in the template (or passed in via $_post) that is NOT being set. Since the error in your first screenshot came in on the activity log, that makes me think it's probably in your header/footer.
When you save the config, the module tries to "validate" the entered S3 credentials are correct (even with the daily backup to S3 unchecked). I'm not seeing any issues on this end - I suspect it is network related if you still getting packet errors.
sbhadauria:still not working, I can not update production
Disable your custom modules and see if it works. No other site has reported this issue, and unit tests are passing 100% for the datastore. I can see your query is missing info, so check your {jrCore_list} calls and calls to jrCore_db_search_items().
I cannot replicate this issue on this end - the DS is passing all unit tests as well. This is coming from your dashboard - have you created any custom dashboard panels? Do you know what panels are active? (look in the database jr_jrcore_settings table for the "dashboard_config" entry for the jrCore module).