If a phone doesn't have find my iPhone app installed, can it still be iCloud locked?

If a phone doesn't have find my iPhone app installed, can it still be iCloud locked? - 1

Yes.

Yes.

DELETE ANY APP THAT CONTAINED iCLOUD.
SOME BAD APP HIDES iCLOUD OPERATION IN MANY LOCATIONS AND STILL RUNNING AFTER THE MAIN APP WAS DELETE. IF IT HAPPENS, YOU NEED TO MANUALLY TRACE THEM ONE BY ONE BY LOOKING AT EACH FOLDERS FILE THAT BELONG TO iCLOUD.
DUMP THEM AWAY AND NEVER INSTALL THIS TYPE APP ANY MORE.