RE: Minimum Powder charge?
Knowing what rifle you have, caliber, projectile, etc would help...
I would say for deer and a .250 gr .451 caliber saboted bullet out of a .50 caliber around 65-70 grains of Pyrodex or Goex, although I have heard of guys using 50 grains and a patched ball for deer within 50 yards...
In my Knight disc, I use 90grs of FFF Goex or Pyrodex R-S and frankly, it's more than enough...Remember the 45/70 used 70grs of real black powder...