1) On Rosh Hashana and Yom Kippur it is customary to kneel and bow one’s head to the ground during the tefillah of Aleinu.
It is biblically forbidden to prostrate with outstretched arms and legs on a stone floor. Chazal forbade complete prostration on all types of floors (carpeted etc.) and they forbade even kneeling (without outstretched limbs) on stone floors. (M.B. 131:40)
2) Therefore, if the shul has a stone floor one must cover the surface upon which he kneels. (Tomorrow we will iy”h discuss what are must one cover) (See Shulchan Aruch 131:8 and M.B. 40) There are some opinions who maintain that it is preferable to cover the floor no matter what material it is made of. This is the why the common custom is to cover the ground even if it is carpeted. (Mateh Efraim 621:14)
3) The poskim explain that a separation is required between one’s face and the ground, not a separation between the knees and the ground. (See Avnei Yashfei 2:7:5 and Netai Gavriel R.H. page 393)
4) When kneeling during davening on Rosh Hashanah and Yom Kippur one may use his tallis as a separation between his face and the floor. (Elya Rabba 131:14 and Shaar Hatzion 44. For further explanation see Avnei Yashfei 2:7:3)
5) Women are included in the prohibition of kneeling on the ground. Therefore, if a woman kneels on Rosh Hashana she must cover her face. (See Chinuch 349)
6) Some women have the custom to kneel and some do not. One should follow her custom. (See Rivevos Ephraim 3:421:2, Beis Avi 3:72 and Netai Gavriel Yom Kippur)