What is appropriate for a Global field in terms of site speed?
I can't speak on the speed impact of having lots of content in the Globals, but the use cases you have described don't really seem suitable for Globals.

I would instead recommend creating Sections for each of these (Testimonials, Awards, The Team) and have an entry for each item.

We use the Globals section (for example) for setting the clients phone number, contact address, email address etc. Just little pieces of information that can be re-used. Quite considerably different to the large content sections you have described.