My research was focused on the efficacy of a, at the time, novel off the shelf product providing 100mg of caffeine per dose, taken immediately prior to exercise (as directed). So I personally did not look into any of those questions, but there are certainly many others who have! A quick google scholar search on ‘caffeine ingestion timing’ will keep you busy for days (trust me, I’ve been there!).
As with any research a meta-analysis or review will give you the best bang for your buck.