の - questioning and confirmation


I learned the grammatical structure of の for questioning (and explaining)
things a while ago, but the exact meaning and which gender uses it has kind of
confused me.

Here are a few varied sentence I'd first like to confirm whether my
understanding of the meaning is correct (I've translated them based on the
feeling I'm get when I hear them):

`暇があるの？` - You have free time? (I thought you didn't)

`暇がないの？` - You don't have free time? (I thought you did)

`暇があるんじゃない？` - (But surely) You have free time don't you? (Confirming as if
you know they don't) - do I need a の at the end?

`暇がないんじゃない？` - (But surely) You don't have free time don't you? (Confirming as
if you know they do) - do I need a の at the end?

Isn't `暇があるんじゃないの？` not used because it doesn't make sense / sounds weird? And
then should you add `か` to the end because it sounds a little feminine or
replace `の` with `んですか？` or `のですか？` to be more formal?




Explanatory の is gender-neutral. You can say 暇があるんじゃないの safely in informal
settings, regardless of your sex, when you highly suspect the listener has
some spare time.

As your textbook probably explains, の is used to seek clarification. You
usually need some context before making a の-ending question.

  * 暇(が)ある？  
Do you have time?

  * 暇(が)あるの？  
(That makes me wonder, so) do you have time?

