Hi Alfredo…I’m here to help you out. My first question would be, did you create a custom menu or using the default menu (pages only)?
Jetpack is just one option of a few, but jetpack also contains a lot more built in plugins of different things. For the Edit CSS, it adds this to the Appearance menu in the admin which you can use to override any CSS from the theme. Basically it will create a new stylesheet with your changes, in turn, helps when you update the theme at any point without losing your modifications. However, a child theme is needed if at any time in the future you decide to edit the actual files of the theme.
It should not matter if you are using the child theme or the parent theme, Jetpack will work for both as the child theme simply inherits everything from the parent theme’s CSS and functionality. I believe it would take over css changes you add to the child theme (but you may want to try that because off hand, its only my guess, but I don’t see why it shouldn’t.
About the customizer and any menu CSS overrides you do, the overrides should work. It depends on where the new stylesheet from jetpack loads. If it loads after all theme styles including those in the portion of your page code, then yes.