Since we dont hire 3B Coaches & Fielding Coaches to our Minor League teams, do our ML ones affect the progression of our prospects in the Minors? Thanks!

Fielding coaches definitely affect every level of development which is why they are so coveted. Not sure about 1B and 3B coaches, I'd guess that they only affect the ML system based on the descriptions in the Coaches page within the Players Guide: https://www.whatifsports.com/hbd/Pages/Main/PlayersGuide.aspx

First and third base coaches only affect your major-league team. prezuiwf is correct regarding fielding coaches. They affect every level of your system. Thus, if you hire a fielding coach with bad fielding ratings, not only will your major-league defense suffer, but you will stunt the fielding growth of your prospects.

I don't recall where (and too lazy to look it up), bit there’s a spot in the rules or the players guide where they describe the fielding coach as a traveling fielding instructor. He’s hired at the major league level, but he is truly a coach for all levels. Preziuwf is right that this makes good FIs highly coveted. But it’s not the only reason - they’re also a hot commodity because if they have a decent loyalty rating they’ll automatically renew their contracts at $750,000 per year.

Bullpen, first base, and third base coaches do not have any effect on minor leakers except during Spring Training, when the prospects in camp all get to work with the ML coaches.