Yes, Home Depot has 12 packs of just that size anchor and screw.
Yes, i have used this anchors on various types of wall and it working very well.
My house is completely dry walled with 5/8" drywall, and I had no problem using these.
Generally no... It depends on how thick the underlayment is, but almost all tile assemblies the tile is mounted on a thin concrete sheet, or underlayed with plywood... This will end up being too thick for these to properly expand and lock in place. I would just hang the safety bars with an aggressive screw that's long enough to really grab onto what it is screwed into... I really like the Stainless Steel Torx drive screws Home Depot sells for things like that.
These will work as long as the wall isn't much over 1/2" thick... 5/8" would be the upper limit on wall thickness.
Ummm... It's a 60 pack, so there are 60 of them in a box. Half will be the larger size screw, and half will be the smaller size screw. So 30 of each size screw, since you are apparently not great at math.