The recipe doesn't look OK to me, intuition suggests glycerol mixed with a concentrated sulfuric acid will get carbonized, leaving a black mess.
I am not sure order of mixing these acids makes a real difference - yes, when diluting them they should be added to water, but that's because dilution produces heat. Just mixing acids shouldn't be that exothermic.
In general when dealing with concentrated acids it is best to work in open air or under fume hood.