Yes. Basic emacs keybindings work pretty much everywhere in macOS. I have run into a couple of apps that don’t behave correctly, but 99% of the time they work.

Yes. For me, on all MacOS versions from Catalina to Sequoia, the basic Emacs keybindings listed here work almost* throughout the operating system: https://support.apple.com/en-us/102650

I don’t daily drive VSCode but I use it for teaching, and then basic Emacs keybindings like C-n and C-a and C-k work pretty much everywhere, from the command palette to the code editor, without any plugins.

I also don’t use Chrome as my daily driver, but keybindings like C-a/C-e certainly work in both text areas and address field, or I would have remembered it as one of the annoying exceptions. I do regularly use a few Electron apps, which are based on Chrome, and it does work fine there.

*: There are a few apps that deliberately break the Emacs keybindings. Microsoft Office is one of them, since they insist that Ctrl keybindings on Mac should do the same as it does on Windows, which is extremely jarring if you rely on the Emacs keybindings everywhere else.