Advanced Physics $-$ fluid dynamic force

Please kindly show me clear steps and explanation, thanks a lot!

Exercise $8$

A water droplet with a radius R$=0\mathrm{.}12$ mm falls into air at a temperature of $20$C$.$

a$)$ properly establish the equation which gives the evolution of the speed over time b$)$ determine the limiting speed of the droplet

c$)$ determine the time it takes for the droplet to reach half of its maximum speed and the time to reach $99\%$ of its maximum speed

d$)$ determine the equation which gives the evolution of the position of the droplet over time $($there is only one dimension$)$

e$)$ determine the distance travelled by the droplet to reach $99\%$ of its maximum speed

f$)$ calculate the work done by the force of gravity for the droplet to reach $99\%$ of its maximum speed and the work dissipated by the force of friction