Maximum density of $H_2O$ is at the temperature

$A$ thermoelectric thermometer is based on:

$A$ certain liquid has a melting point of $-50^{\circ} C$ and a boiling point of $150^{\circ} C$. $A$ thermometer is designed with this liquid and its melting and boiling points are designated at $0^{\circ} L$ and $100^{\circ} L$. The melting and boiling points of water on this scale are

In the definition of 'calorie',one calorie is the heat required to raise the temperature of $1\ g$ of water through $1\ ^oC$ in a certain interval of temperature. The temperature interval is

Answer the following:
$(a)$ The triple-point of water is a standard fixed point in modern thermometry. Why? What is wrong with taking the melting point of ice and the boiling point of water as standard fixed points (as was originally done in the Celsius scale)?
$(b)$ There were two fixed points in the original Celsius scale as mentioned above,which were assigned the numbers $0^{\circ}C$ and $100^{\circ}C$ respectively. On the absolute scale,one of the fixed points is the triple-point of water,which on the Kelvin absolute scale is assigned the number $273.16\; K$. What is the other fixed point on this (Kelvin) scale?
$(c)$ The absolute temperature (Kelvin scale) $T$ is related to the temperature $t_c$ on the Celsius scale by $t_c = T - 273.15$. Why do we have $273.15$ in this relation,and not $273.16$?
$(d)$ What is the temperature of the triple-point of water on an absolute scale whose unit interval size is equal to that of the Fahrenheit scale?

The saturation vapour pressure of water at $100^{\circ}C$ is ........ $mm$ of mercury.