They need to be kept in groups, all of them. However, they definitely do differ in their behaviors. Some are very placid, while others are very frisky. Albino corydoras are known to swim around the tank at all levels. Behaviors differ between species and individuals, but this makes them interesting.
Not a chance, unless they are fry. And even then, it's highly unlikely. Very peaceful, lovable fish. I hope you get them. Make excellent bottom feeders.
IMHO, corys are the perfect community fish. They are content to socialize with their own kind and bother no one. Since they primarily live on the bottom of the tank, they don't compete with other fish for food or territory.
The only thing they specifically need is the companionship of other corys, since they are a schooling fish. You will be happy to see that, unlike many of the other schooling fish, they interact with each other and seem to enjoy each other's company, especially when they are young.
IMHO, corys are perfect citizens in any community tank.
IME if a cory hurt a fry it would be accidental. Definitely peaceful and entertaining fish. Just remember to keep them in groups of at least 4-6, preferably 6.
I agree with everything above. Watch out for Scleromystax (formerly Corydoras) barbatus, the males can be a bit nasty, it's virtually the only territorial Cory.