The first thing you need to do is to make sure that without any wax seal, or if that blue thing was the seal, to remove it and see if the toilet will sit without rocking on the high portion of the flange. If it does, you really need to fix the flange. It's not unusual for a toilet to rock a little on the floor, but there must be a gap for the wax ring to seal the flange rather than rocking on it...if it isn't rocking on the flange, you still need to shim the toilet so that it is stable prior to adding the wax to make the seal. If it's not touching the flange, I'd consider stacking some washers or making a shim underneath the high sides so you can then screw it down to what's beneath...if the holes line up on the tile, you'll probably need a special drill bit to make a hole. The best one is probably a diamond core bit. When using one of those, keep the area wet to keep the diamonds from flaking off from overheating, and keep in mind, those diamond chips are more like grinding the hole rather than cutting like a drill in wood.
You do want the flange well anchored to the floor as well. With a tiled floor, the flange bolts to the toilet help to center it, but won't keep the toilet from moving if it is bumped because of the smooth surface of both the toilet and the tile. So, partly to resolve that, and to meet most code requirements, they want a caulk around the toilet's front 3/4'ers or so to both seal if from crud getting beneath, but also to help hold it in place.
I would be clearer what's there with a picture...use the 'Upload a File' tab to get it from your computer to this site.
