The essential oils of citrus fruit (especially orange and lemon oil) found in the rinds of the fruit contain certain hydrocarbons that are very effective in destroying the links between polymers in plastics, and a powerful solvent on oils and resins. This is why a lot of cleaning agents today contain citrus oils, and why the oil so easily pops these balloons. It's basically eating away a hole through the plastic.
A good example, if you have enough of it; put a few drops of lemon oil on a piece of gum if it's stuck in a carpet and wait fifteen minutes. It should become liquefied enough to come right out.
Not necessarily, considering that orange oil doesn't eat dissolve organic materials like flesh so easily, but in high enough concentrations it can become irritating to sensitive areas such as the mucous membranes. Your eyes are more tearing up because oil doesn't mix well with water, and they're trying to rid themselves of foreign substances.
Otherwise it's quite healthy and stabilizes blood ph levels, and regulates several hormones that affect stress and mood.
Slightly unrelated, but when I was in fifth grade some guy stuck a wad of chewed gum inside the cartridge of my Pokemon Emerald. I spent days trying to get it out before finally giving up and buying a new one. **** that guy.
Most acids can't dissolve plastics. And there isn't any citric acid in the essential oils. It's actually slightly basic. (The opposite of an acid, and it's why the rind has a bitter taste)
Orange oil is great. I use citra-solv (which is essentially orange oil) to clean mod podge and hot glue off the tables in my classroom. It got pine sap out of my hair once too.