My issue with signing out out of every app on close is sovled
For some reason, after an upgrade, all those options in the picture were selected even though I have selected only first two. Now it works again. Something changed my settings.
Using mouse to close last tab does not trigger browser close anymore.

However, after 200 new versions, Maxthon still forces an icon on the desktop without my permission, and the bug where the number of hidden tabs is not properly shown is still there.
I suppose this is something that will never be fixed 🙁