As a mature student who has done part-time, live in College and live locally -
a) it will have a huge effect on the Cambridge experience, though you may not care
b) you need to leave an additional hour to get to and from Trumpington P&R at any time schools are open or rush hour, unless you cycle
c) just because you 'want to' isn't likely to be accepted by your College. You will need to show a very real domestic need. An 'easy commute' from London is frequently cited and I've never heard of it being accepted, but clearly don't know all cases.
Cambridge is simply a residential university. You might get the right combination of course, Supervisor, College and Senior tutor, but without something like a disabled partner combined with care responsibilities or similar, it's not going to be allowed.
You can use any email address to write and ask permission.