1. "Smithing" comes from the same root as the verb "to smite" -- that is, to hit. "Forging" comes from the Latin "fabricare" by way of the Old French "forgier", to make. Both have long histories in English -- early 13th and late 14th centuries, respectively -- and they are, as ThomasPowers notes, essentially interchangeable. (It should be noted, however, that some modern smiths use "forge" to denote actual deformation of the cross-section of the metal, as opposed to bending or twisting.)
2. What ThomasPowers said. If you have a chance to get yourself some classes, DO IT. If they teach forge welding, so much the better. Forge welding is one of those things that is easy to mess up, and having an experienced smith who can see your mistakes and help you correct them is well worth the investment in time and cash.
3. You are limited to what you can forge with your particular degree of skill and muscle. Exceeding either will cause you an injury. If you're not getting a power hammer and you don't have access to a striker, consider either building yourself a treadle hammer or figuring out some way to hold your work while you yourself use a sledgehammer on it.