Vinegar is a good idea. Add some to the white material, if it gives some bubbles it is probably Carbonate. To be sure the obtained gas has to be conducted in a solution of Calcium hydroxide. Here it will give a white precipitation, which disappear after some time gas treatment.
It can be also Calcium nitrate, if the material is found in Toilet rooms, stables, farms, etc.
Calcium I think you cannot detected easily at home. need some test stripes or an complexometric titration.