Carrd is deliberately a one-page builder, which makes analytics setup unusually simple once you're on a plan that supports custom code — one embed, and the entire site is covered, since there's only one page to cover.
No — custom code/embed functionality is a Pro-tier Carrd feature; the free plan doesn't support injecting arbitrary scripts.
No — that's the advantage here. A Carrd site is one page, so adding the script once covers the entire site with no per-page repetition.
Minimally — the script uses defer and Carrd sites are already lightweight, but it's still worth confirming the page feels instant after publishing.
A code embed element on the page typically renders inline where you place it rather than in <head> — placement earlier on the page is generally fine for tracking purposes, but check your specific Carrd embed type.