Regarding the answers to the application questions; I would suggest answering the to the best of your ability, and carefully considering what you would like to include.
During my assessment process 2 years ago, the answers formed a key component of the overall picture that I presented as an applicant. They were also referred to at both interview stages.
It is not simply a case of "pass - move on to the next round". They will be looked at again, and, should you make it to Heathrow, they will be critical.
In fact, when you think about it, it is the only voice you have in the boardroom when the big decisions are being made - Your interview is not transcribed; your test scores are just that. So I would suggest putting some thought in about what you'd like to include and to what level of detail. If you need to research, then make it so. The word limits are quite restrictive. Re-read what you have written. Make it better. Leave it overnight, and repeat.
Take your time with it. Yes - BA may close the application window early, and have done so before, however there invariably is a warning email sent to registered applicants to fell you to got it submitted. There is no rush.
Good luck.