My text book says that parabolic dunes consist of consolidated limestone grains, but I wondered if they have sand grains too, so I googled this issue and found that they consist of sands, but I am still perplexed, do parabolic dunes have both sand and consolidated limestone grains or they only contain one type of grains? And do they form exactly as other types of dunes (barchan dunes for example)?
"Sand" is generally made up of whatever eroded rock type is nearby, minus the most easily eroded (and windswept) components. Typically, dunes are made up of highly resistant quartz grains, like the stuff that blows off of white sand beaches, for example, or feldspar sands which are even more erosion resistant (in certain cases). There are also very soft white gypsum sands in New Mexico who owe their existence to a nearby, inexhaustible supply of gypsum evaporites.
As for limestone sands, I've never heard of it although it's certainly possible given very specific circumstances. Nevertheless, that's not what controls dune morphology. Dune shape is almost entirely controlled by both wind and sand supply and similarly shaped dunes will occur regardless of grain composition if dune-forming components are the same.