Overall page formatting

I think I'd like to have a bit less space between the vocal parts and the piano part...
See:
https://musescore.org/en/handbook/3/layout-and-formatting#style-page

But be aware that your vocal and piano parts contain more content in some places than others.
For example, here's the system starting at measure 49 compared to the system starting at measure 6.

You've got dynamics, lyrics, chord symbols - all (automatically) use more space, compared to measures 6 - 11.

(I'd like) ...a bit less space between individual staves.
Perhaps you mean less space between systems rather than staves, in which case you can tweak Min./Max system distance.
(See handbook link above.)

FWIW, for a quick way to get the music more "compressed' on the page, try this:
Go to Format-> Page settings and set the top and bottom page margins to 0.75 in, or even 0.80 in.
You can experiment to see how the music will be "compressed" to fit within those page margins.
Sometimes this works to prevent excessive whitespace at the bottom of a page which could happen when decreasing staff/system distance and another system is too big to fit into that space at the bottom of the page.
See:
https://musescore.org/en/handbook/3/page-settings#page-margins

(Essentially, it can move some of the whitespace from the bottom to the top of the page. Music top margin and Music bottom margin in the Page style settings can do similar.)