minie bullets or minie balls were originally used in military rifled muskets. They are conical shape with a hollow base. No patch is used - they are loaded hollow base down directly on the powder. When the gun shoots, the burning powder forms gasses that expell the bullet. In the process, the hollow base expands and "grips" the rifling.
Many of the newer BP rifles utilize a conical type slug and they are often referred to as minies by some folks.
In regards to the 50 versus the 54 - I've had both and both are good calibers. Either would certainly work on deer - if I anticipated bigger game, I'd probably go with the 54. If you cast your own balls, you aren't going to get a whole lot more of 50 caliber one 54 caliber out of a pound of lead - I've never figured it out but I suppose someone on here can tell you. Recoil - you aren't really going to notice a whole lot of difference - a lot of that is going to depend on the charges you would use in each caliber. I don't hunt anymore. I sold my custom Hawken that I made that was in 54 and I don't have the 50 caliber flinter anymore either. And yes, I do regret selling them. If I was going to get one now, I'd probably go with the 50 but that's my age speaking - more of a mental thing in regards to thinking it might be easier on my shoulder/arm - which really, it wouldn't.
Good luck in your quest and let us know what you end up with. Either way you go, have fun - that's what it's all about. As addictive as BP is, chances are you'll eventually end up with a couple of rifles - and don't forget about smaller game either - squirrels, rabbits, etc. 36 caliber is nice for such things!
If a pair of '51 Navies were good enough for Billy Hickok, then a single Navy on my right hip is good enough for me . . . besides . . . I'm probably only half as good as he was anyways. Hiram's Rangers Badge #63