getServerSideProps runs on the server as the name implies, not on the client as the page does. You'll want to just fetch from your db or whatever that query does in that function.
Nope, the opposite. gSSP will block the page load until that function returns, which is going to wait for the db call. If you use the trpc query, it'll be in a loading state until the data arrives but won't block page load.
I'll mainly use it when I want to restrict pages to authenticated users or users that have a certain characteristic (like permission level), that way they don't see the page at all and you can easily redirect them to something like /login