You can suppress the message by creating a new config with log level ERROR for class org.apache.felix.jaas  OR configure rotation as per your need. At this point I have less involved in Solr side for right recommendation.  You can file a support ticket and attach the logs, thread dump. will validate...

Have you defined any custom sorting index Or overlayed oob component like cf,... ?  Because jcr\:lastModified_string_sort sounds suspicious & should not be there. Additionally it is not multi field.If you have not overlayed then Please file a support ticket with below informationOutput of http://hos...

Just a guess. You can ignore it.

Sounds like many referenced file deleted from blob store. You need to restore missing blob from backup Or create an empty file Or identify the file & take from other environment.For now let us identify missing node & then will decide about next steps. Please follow below steps.*) Login at http://loc...

sounds like you are using custom authentication handler. please disable them & verify. Or firewall restriction try http://www.aemstuff.com/#article971

can you check in index defnition compactVersion set to 2? If not change, reindex and verify.

For service pack you can use http://www.aemstuff.com/tools/coi.html Or manually verify in welcome screen.For hotfix you can check status at [1].[1]   http://host:port/crx/packmgr/service.jsp?cmd=ls

It should work. May be your testing is not accurate & missing something.  How are you testing?

follow https://helpx.adobe.com/experience-manager/kb/performance-tuning-tips.html

5.6.1 & AEM6 had issue . Tracked at GRANITE-3909 which is resolved through hotfix NPR-3590.  AEM 6.1 includes the fix.  File an support ticket with logs & query triggered will help to find is product issue or other.    Generally it happens if you have nested groups & get into redundant or conditions...