Cotton is significantly less dense than iron. Therefore if you have equal volume samples of cotton and iron, the iron sample will weigh more than the cotton sample.
A substance's relative density is the ratio of its density to that of liquid water. You are taking two quantities with the same unit and dividing them. This will cancel out the unit on the top and bottom, leaving you with a number that has no unit.
Inflating a balloon puts it under an awful lot of pressure. The material must remain pretty durable throughout in order to sustain that much stress. Any weak spots inside the balloon will eventually give way; the balloon will then rip and pop.