I strongly recommend that you learn your states hunting laws. Each state is different. Some states require a .36 caliber muzzle loader or larger to hunt large game. Other states require .50 caliber or higher. There are some states that even allow the use of scopes or red dot sights on muzzle loaders. If you are ever in doubt about any aspect of hunting in your state, a quick trip to the local Department of Wildlife will answer your questions. It is best to know the law than to plead ignorance. Every game warden I have met is professional and helpful, but they have a job to do. They are expected to enforce the laws for their state.
Most states allow muzzle loaders to hunt at the same time as bow hunters. This season is usually earlier than the center fire hunting season. This is a huge advantage for both bow hunters and muzzle loaders. The game animal has not felt the pressure of hundreds of ATV hunters flooding the area. There is a less human presence in the area so this might make the animal less likely to spook. It is early in the year so the weather is milder and hopefully less rainy or snowy. By hunting during the muzzle loading / bow season, I have noticed that every person out there hunting feels the same way. There is a conscious effort to reduce noise and human presence. Both hunting styles need to be closer to the game for a successful shot, so they support each other by making their presence less felt by nature.
Any animal can be hunted with a muzzle loader. A well placed round can bring down a deer, but most states require a specific caliber or larger depending on the game animal hunted. The most common caliber for large game hunting is .50 caliber. It is a bit large to be hunting small game such as rabbits and squirrels, but it is an effective round for deer and elk. If you are casting your own ball or Minie ball rounds, the larger the caliber the more lead used per shot. A smaller caliber weapon will allow you to hunt smaller game more economically, both by powder used and lead used to make the round.
Each state has a different view on the possession of an additional firearm for self defense. Some states will not allow the hunter to possess ANY other firearm other than the muzzle loader being used to hunt with. Some states allow a muzzle loading single shot pistol to be carried. That is, a single shot pistol, not a cap and ball revolver similar to the ones used in the U.S. Civil war. Some states allow for a personal sidearm for self defense. Once again, I strongly suggest that you do the research into your state muzzle loading laws. I know you don’t want your self-defense pistol impounded over a mistake.