after which round are the most girls cut?

You are not "cut", you don't "cut" - it is pure ranking. Your name may have been further down and the girls ahead of you on the list may have also ranked that sorority higher. They are limited on how many girls they can bring back.
If they are being ranked each day very high they have a high return rate. Therefore they will not be bringing back as many girls as some groups.
Regarding making it to sisterhood day and making it to prefs - that is not always true.

If you make it to pref to your legacy sorority, does that mean you are automatically on their bid list? Does it depend on the sorority? I have heard conflicting views about this. Thank you!

Some sororities do offer less back after Philanthropy day. I would say that the majority of girls who keep certain groups after that day have a better idea of who wants who. I knew one girl who had 7 invites back and then 3 and she kept those 3 the rest of the time through pref, so you will be able to gauge soon as to who is interested and vice versus. Important however, if you do not get back the group(s) you wanted, but you got several groups back...I would try to see beyond the hurt of being dropped lower and try to imagine you in one of those groups that want you. In all probability this is the best chance you will have of pledging than at any other time. Many sororities will be at full quota and not have open rush, so look hard. If you don't want any you have left, but accept a bid and then drop out, please don't take up the space of someone who does. There's nothing wrong with not being in a sorority if you are unhappy with the choices.