Hi,
If you deactivate the Stats module, we’ll no longer record any stats information for your site. That module is pretty lightweight though.
There aren’t any issues with RPs. We added a bit of caching to them to make them faster. For Related Posts, what happens is your page should fully load. While it is finishing loading/after it is loaded, we send a request to WordPress.com with the page you’re on, asking for related posts. WordPress.com replies with a list, which is then parsed into the picture, title, etc and inserted into your page.
When clicking a link from Related Posts, the same thing happens, but with an added parameter to exclude the particular post that you just came from (so visitors would be led down a new path of awesome content).
In both cases, Related Posts should be loading async of the rest of the page—e.g. nothing should slow down on your side since we do it all in the background while/after the page is loading.
I’m not sure how RP impacts the percentage with P3 (nor aware of exactly when P3 declares a page “done”). If they’re counting ALL of the time for Related Posts, then yes, it’ll look high, but it is designed to not slow down a visitor visiting your site, if that all made sense.
Cheers!