Yggdrasil beat my to the difference between H+ and H2.
I have to agree with the no one should have to memorize the periodic table. The thing is, when you practice these things, you shouldn't have to physically put effort into memorizing the periodic table. Things should just come second nature, and you automatically know what the charges are and the formulas for that matter. It's like driving a manual, at first you have to put a lot of thought into it, but then after awhile you don't even realize your foot pushing in the clutch, and your hand shifting the gears.
The periodic table though and a list of polyatomic ions are excellent reference tools for when you encounter something you don't use often.
A good thing to do though after you think you've finished writing an equation is to go back, and look at the charges to make sure everything is neutral. Then once you do that you balance it, and then double check to make sure you have the same number of each atom on each side.