(i) Ice has a cage-like structure with large empty space between the molecules. As water is warmed from 273K (melting point of ice) onward, more and more hydrogen bonds are broken. Naturally, water molecules come closer and acquire lesser volume. Hence, density increases. But this decrease in volume is opposed by the normal tendency for expansion on heating.
Up to 277 K: Contraction factor is more than the expansion effect, so there is a net decrease in volume or increase in density.
Above 277K: Expansion factor (due to increase in thermal energy) becomes greater than the contraction effect (caused by breaking of hydrogen bonds), naturally, volume increases and the density decreases. Thus, the density of water is maximum at 277 K.

(ii) This is because of the presence of three -OH groups in glycerol as compared to only one -OH group in ethyl alcohol. Hence, there are three hydrogen bonding sites in glycerol while there is only one in the case of ethyl alcohol molecule. Hence, there are greater intermolecular forces of attraction in glycerol as compared to ethyl alcohol, therefore, it is more viscous than ethyl alcohol.