1. Adobe Illustrator, Photoshop or SAI (Illustrator is preferred for vectors however.)
2. No, you may have confused iPad with a drawing tablet. A drawing tablet is generally preferred for digital art. Here's a link to the Wacom website. They make drawing tablets. I have a Wacom for my art. Peruse the site and you'll understand why I think you got confused with an iPad and a tablet. http://www.wacom.com/en/us?gclid=COyz_MO8ub0CFUJqfgod_YgAfw
3. A vector is a resizable image similar to that of a font in a .ttf format. A vector, however, does not require it to be in a .ttf format. Here's an example of a vector. http://th02.deviantart.net/fs70/PRE/i/2012/225/7/9/twilight_sparkle_by_sulyo-d5ar835.png