Explanation:
#1 is wrong because if the first character is not lowercase, it stops and returns false, ignoring all the other characters. It can be fixed by removing the else: statement and moving the return False statement outside of the loop.
This is efficient; if one lowercase character is encountered, the function 'knows enough' and can return true. Only if no lowercase is encountered it has to loop all the way to the end.
You can try this out on repl.it.
Many of the others functions have problems in them. #4 looks OK.