I absolutely love my two flocks of geese! I've raised them on and off for the past five or so years and getting back into them recently was one of my better poultry-related decisions. The link in the above post is very helpful. Here's my two cents on your questions.
1. Some are, some aren't. Aggression can depend on the breed, time of year, how they were raised, etc. I keep Pomeranians and Dewlap Toulouse. The Toulouse are far more gentle-natured than the Poms. The ganders don't hardly squabble at all during breeding season, whereas the Poms have some pretty good showdowns now and then. None of mine are aggressive towards me. I've handled all of them since they were babies. Allowing goslings to imprint on you while they are young is a big step towards very friendly geese. That means spending time with them and hand feeding treats etc. That's not saying if you don't they'll be mean, but if you do there's a good chance they'll be more like a feathered dog than a bird!
2. As far as incubation and hatching, waterfowl are a little different. Eggs can benefit from higher humidity and take 28-35 days to hatch. Hatching geese is of course more similar to ducks than with chickens. That link has some great details. As with all waterfowl, geese prefer to breed on water. Fertility can be an issue in some breeds and compared to some breeds of ducks and especially chickens, geese are far more seasonal layers. Both the males and females are also incredibly devoted and protective parents.
3 and 4. I know plenty of people who keep geese with other species of poultry. My personal opinion is to give geese their own space. Geese are territorial by nature, and I've always thought they appreciate their own space. Not to mention, they are one of the biggest birds in the barnyard--and they know it too. That being said, they can tend to be bullies. They also become increasingly territorial during breeding season. So I've always felt giving them their own pens is easiest on everyone. However as I said before, plenty of people keep them with other species, especially ducks. I would just keep an eye on things, particularly in the spring.
Geese are hugely rewarding to keep, and once they feather out are virtually self-sufficient if given adequate pasture and protection from predators. They are extremely intelligent as well. They make excellent watch dogs and, if you put in a little TLC, they are actually very good pets despite their reputation.