1. We'll find out for the press conference, however the Dragon will be modified. The Dragon already is certified for six months on-orbit (expeditions to the ISS), so the vehicle itself can handle it. A modified Dragon to be able to handle solar flares and the stress of a 501 day mission will be developed for it. Look at the ISS though, it uses filtered and recycled air and it's been manned since 2001.
2. Not as much as you think, it can be done cheaply, around 250 million dollars. You're looking at this from a government run standpoint, where it takes a spacecraft the size of a football field with 12 people. That would take billions of dollars and years of development, with hundreds of thousands of people behind it. You have to pay those workers, you have to commit R&D to develop a brand new spacecraft, you have to develop a launcher to accommodate that spacecraft. The Falcon Heavy exists and can certainly take a Dragon beyond LEO.
3. No, but the public will be livid with anticipation at such a monumental event as going to Mars and possibly even Venus. Look at the interest during the Curiosity landing - the public loves this stuff. It's dangerous, new, and exciting. The entire United States and rest of the world stopped the moment Apollo 11 landed on the moon, they will do it again.
4. This isn't landing on Mars, it's a flyby and return.
5. Again, this isn't landing on Mars.
A mission like this needs to happen for us to be able to make that next step of actually landing on Mars. It needs to be proven. The ISS and Mir proved (in the case of the ISS is about to prove) that we can stay in space for a year. This will prove we can stay in space for longer, in a more confined space, and will prove a manned spacecraft can go to different planets without sterilizing the crew and vehicle.