> Ok, what kinds of problems are they?

> And ideally - what does a simple solution look like in F-star?

RTFM

Or to explicate on this point: find a section in the table of contents that looks interesting to you, go to the respective section, and look at a code example.

> Set me on the path to installing the thing (ideally above the fold)

How to install this thing:

1. Read https://fstar-lang.org/index.html#download

2. Go to the GitHub page linked there: https://github.com/fstarlang/fstar/releases

3. Download F* for an operating system of your choice there.