Bounty, Dentyne, & big breaths
My nose gets runny too sometimes, especially when I ride at night. I carry one or two squares of Bounty paper towels. Even if they get moist from the sweat coming through my jersey, they won't fall apart.
For keeping my mouth from getting dry, I chew gum. Just having something inside your mouth makes you produce more saliva. Plus the gum encourages me to keep my mouth closed and breathe through my nose. Occasionally I'll breathe in through my nose and out through my mouth, but for the most part I try to keep my mouth closed.
As for losing your breath: try to control your breathing! I know it will seem impossible as you're gasping for air, but just try it. It's *much* more effective (in terms of getting oxygen into your lungs and blood, and getting carbon dioxide out) to take slower, deep breaths than to take quick shallow breaths. The same exact volume of air, taken in deep breaths, will deliver more oxygen to your lungs than if you took it in a greater number of shallow breaths. Also be sure to exhale deeply, because it's the accumulation of CO2 (carbon dioxide) in your blood (not just the lack of oxygen) that will make you panic and breathe faster than you really need to.
Another thing that's helped me a *lot* is to plan ahead. If you see a hill coming up, try to relax and take lots of really deep breaths in preparation for the climb. When I started using a heart rate monitor, I noticed that my heart rate would start to go up even before I got to the hill, probably because I was nervously anticipating the climb. Now I just breathe deeply and stay relaxed so that I'm well oxygenated and ready to attack it.
I hope some of this helps!
~Cari