What happens if you play the game solo, using only the main character? Will he gain more experience and be able to reach level 12?
There's no way. All experience is distributed the same. For example, gaining Wyll later on, you should be lvl 3 by then. When he joins he will also be lvl 3. If anything it will cripple your xp in fights where there are other parties involved fighting the same thing, they can steal xp from you if you never landed a hit.
Another way of explaining it is, at the very beginning on the nautiloid when you make your first kill with Laezel which should be an imp, you get 10 xp, then later get Shadowheart and kill an imp, it's still 10 xp. Each character will get the same xp from that kill, it isn't divided.
If you released the brain on the nautiloid and made it follow you, if you have it kill anything before you hit the target, it will steal xp from you. You should be lvl 2 right after the crash.