Hi Stephane,
Do you still have these problems with version 1.3? They should be fixed now, so if you still have them, please let me know because in that case there's something wrong with the new version.
You should be aware that these "persistent" instances of PixInsight 1.2 seem to be due to malwares (spywares or Trojan horses) preventing termination of the PixInsight Core application. I'd check the computer with a good antispyware/antivirus tool.