Can I use hot water towel on the grafts and is it mandatory the transplanted hair to fall?

Yes, you can use the hot towel after 2 weeks. It will increase some blood flow and feels great. It shouldn't have any effect on your grafts at this point either. The transplanted hairs will most likely fall out around the 2 week to a month marks and will start to re-grow around the 3 -6 month mark. 

Yes, you can use a warm wet towel. An FUE is treated just like a regular hair transplant with regard to the recipient area, but the donor area has open wounds which require daily washing with soap and water. Within 3 days of surgery, you can resume full activities, heavy exercises if you wish. The recipient area requires daily washes as well to keep the recipient area free of crusts. I generally recommend the use of a sponge and supply my patient with a surgical sponge to fill with soapy water and press on the recipient area daily. By repeating this daily, all crusts can be washed off without any fear of losing grafts. IF any crust are present, use a Q tip and dip it into soapy water, and roll it on the crusts and that will lift them off without dislodging them, but never rub them, just roll the Q tip on the recipient crust. I like to see no evidence of any crusting in the recipient area and the crusts from the donor area gone in 7-10 days with daily washing.