Tiger barbs and cory cats would not be a good mix IMO.
Not all that often, at least as far as I've heard, but it can be done, even by accident, if your water is right. Check around with your local aquarium club--they should know if one of their members has done it.
Yeah, and neither would the tetras imo.
With a tiger barb only 55 gal you can have 30 tiger barbs in all (says so here http://www.aquariacentral.com/forums/showthread.php?p=1459108#post1459108 ). Personally, I'd have about 20 tiger barbs and 6 giant danios