Is any way to save only from normal mode "out of box"?

Hello,

1) We have ZZ (like :x), and ZQ (like :q!), but if I need just to save buffer without quit from it? Or I have only ability switch to Cmdline mode with ":" and type "w"? I need "out of box" solution from normal mode or from insert mode.

2) How to jump with very minimal keystrokes from insert mode to Cmdline mode?

Thank you!

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