Questions about Billy Summers (I‘m an idiot)

Hi I am halfway through the book and have a few questions I barely dare to ask because I feel they are very stupid. Anyways:

1) Why, if it’s clear from the beginning (and it’s also said so), that the cops will know it was David and that both this ID and Billy have to be given up, does he even bother to begin with with the David ID and why does he bother to blend in? Why not just be a low key Billy, do the job and vanish?

2) Why doesn’t he, when taking the shot, already dress up as imposter Colin? What is the reason for hiding the costume in the toilet and dressing up only after the shot?

3) Why doesn’t he just bring the laptop to the Dalton apartment the day before the shot?

Please let me know your thoughts and help a fellow stupid reader out! Thanks in advance!