Eh, all the studies I've seen that show some dramatic difference have been funded by paper towel producers and used poor methodology. I believe research by the Mayo Clinic has shown that air dryers and paper towels are roughly equivalent for hygienic purposes.
Convenient for me? No, I either stand there forever or leave with semi-wet hands. Paper towels work much faster and more effective, but the decision is made by facilities.
I only know what the Internet says so this may or may not be correct.
1. Inward opening is probably less inclined to disperse bathroom air into the hallway outside.
2. You're probably less likely to smack someone with a door opening into a hallway. (Or course, someone entering might do it to someone exiting a bathroom but most people are probably at least somewhat trained to exercise caution under those circumstances.)
3. If anything, I'd think fire code would favor door opening out given that's the general rule.
I think doors on the emergency exit route always open outwards so that they can open in a stampede. You'd usually have push bars on them instead of a regular handle too.
Your hands dry much quicker under a hand dryer if you rub them together. I see so many people who just leave their hands flaccid and it takes a lot longer