$550
Find one for sale and buy it.
As the US Civil War entered its fifth year in 1865, most infantrymen were no longer using the old style musket type rifles of the past. By the war's end, most soldiers were using either the '58 Springfield or the 577 Enfield rifle musket.
The Internet.
Dangerous game
That depends on which "Enfield" gun it is. The Enfield name applies to several rifles from blackpowder muskets to multiple variations of bolt actions made in several countries as well as a revolver. Values differ based on type of gun and condition. This question is not answerable without a lot more information.
Hunting, shooting, collecting.
Made by who, you need to state who makes it.
A VERY large caliber, VERY powerful rifle. It is the .577 T-Rex.
Martini Henrys of that age were usually chambered for the .450/.577 cartridge which shot a .46 in. diameter bullet. The value depends on the maker, model and condition, anywhere from $100 to $1000.
Here is a good article for you- http://en.wikipedia.org/wiki/.577/450_Martini-Henry
Possibly the .460 Weatherby Magnum, the .577 T-Rex, or the .700 Nitro Express.