Hi Golden
1) Yes !! You can call any mineral, or combination of some minerals , a "stone" ( or better - "rock"). And depending on it's size - "little stone".
2) Every single aggregate of sand is made of the mineral Quartz (SiO2), and was in it's history a single crystal in Granite rock somewhere in central Africa (The sand of Israel) or any other place (for sands in other places in the world).This crystal made a long trip (mainly in rivers) until it received it's spherical form.
3)Quartz is a very hard mineral ( 7 in scale of 10), and therefore it's
one of the last minerals that left over after the severe erosion it suffered. As long the distance as it pass - so it become smaller and smaller . But - measurements in many dunes in the world showed
a pecullar fact: - more than 97% of all the grains in the world are bigger than 0.2 mm. Many theories published about this effect , but there is not any good explanation.