1. Replaying another CG scene from the CG room should replace the image and thus get rid of the unwanted image.
2. On android you can use the new apk file to install the game again, which updates your game files without deleting your saves. On other systems you can download the full new game version and move the save files from the www/save folder of the old version into the same folder of the new version.
If you have the last version, you can also use "update files" to upgrade without having to move your save files. Please make sure that you haven't skipped an update, or you'll be missing files and get bugs as result.
I made a video about updating on windows here:
3. For the queen of Begus you need to have the second political meeting and then check the paperwork on the desk in your bedroom.
The king of Amagal requires that you have Chiyo with her magical knowledge high enough to repair the teleport in the Ying or Yang Tower. (I always forget which one is which. ^^")