Why do we titrate from a colourless solution and why should we remove unused sodium hydroxide from the burette as soon as possible?
Why is it preferred to titrate from colourless to a pink solution rather than pink to colourless?


It is much easier to detect the appearance of a color rather than the disappearance of one. 

I really liked the large white ceramic ringstands for phenolphthalein titrations. The bright white background really made it easy to monitor the titration. At first you can just let the base (sodium hydroxide) pour into the solution as your are swirling the solution. You just get a pink cylinder where the base is entering the solution. As you get nearer to the end point then the color will start to go out more into the solution. Finally you do drops at a time, and then a partial drop. 


  Also, why is it advisable to remove NaOH from the burette as soon as possible after we are done titrating?


Sodium hydroxide is a strong base and it will etch (dissolve) glass given enough time. If you're using a burette with a glass stopcock the sodium hydroxide can also weld the stopcock joint. 

I'll add that you never should pour the unused sodium hydroxide back into the stock solution. Any that you don't use is waste. You want to avoid any possibility of contamination.