From what I can tell, "Leopard Puffer" is another term for Green Spotted Puffer. If that's the case, they need brackish water, should be housed by themselves because they can be really aggressive, get about 6" or so and need a diet full of crunchy foods like shrimp and snails.
Puffers range in size from the 1" dwarf puffer to the three foot Mbu puffer, so the tank size really depends on which species you want to keep. For a single green spotted puffer, I think 29g would be a minimum, but even then you'd need hefty filtration as they're messy eaters.
Brackish water is water with some marine salt in it, ranging anywhere from just slightly salty to almost full marine salt levels. There aren't many commonly kept aquarium fish that live in brackish water, but some examples are green spotted puffers, scats, monos, archers, and many gobies.
It depends on exactly what fish you're keeping. Also, green spotted puffers usually like less salt when they're young and eventually almost full marine when they're full grown. I read somewhere that 1.005 is good for young ones, but eventually you will need as high as 1.018 (some say even more). This is marine salt mix, not regular aquarium salt.
Batman's right. In the wild they're born in freshwater and slowly make their way down river as they grow up into saltier water. When batman says 1.005 he means specific gravity or SG. It's what is used to measure how salty water is. Regular salt (or "aquarium salt") isn't the right stuff for making your water ocean-y, you can buy the proper stuff in the marine section of your LFS, I buy something called Instant Ocean.