Why do we use glycerol bath, instead of water bath in melting point determination? If glycerol were not available, what can we use instead? Suggest at least three liquids.

Glycerol, a common coolant fluid, is used to determine melting point because unlike water, glycerol has a very high boiling point. Water will boil off at 100 degrees Celsius in standard pressure, whereas glycerol stays liquid up until 290 degrees Celsius.
Other liquids you could use would be best with similar properties. This means liquids like oils, which can stay liquid at high temperatures, will be great for melting point determination. Motor oils, which function around the intense heat of an engine, or cooking oils, which far surpass the boiling point of water, would work well here.
For things that need to be even hotter, liquid mercury could be used, as it has a boiling point at 355 degrees Celsius.
If you find yourself needing just a bit more heat than your liquid accommodates, you could add a salt to raise the boiling point slightly.
http://www.aciscience.org/docs/physical_properties_of_glycerine_and_its_solutions.pdf