Trying to fill in cell if a specific cell has number, then copy from one of three cells in order

I'm trying to make a scheduling calendar for work and we only use Microsoft.

What I'm looking to do, is if the first Sunday of a month is the 1st (and only if the number 1 is the 1st Sunday of the month), I want it to copy the name from either the last Saturday or the 2nd last Saturday of the previous Month or in the rare case the 28th of February ends on the third last Saturday of the month (which ever is first in that order). The link to the file is https://1drv.ms/x/s!Au-Zw7vw3BtFmBad5lv2eMn3OpRW?e=mucia4 for you to play around with and see if you are able to make it work. I appreciate all the help.

Bonus question.. Since I'm creating this calendar from scratch to fit my work needs, If someone is able to input the right formula to make the calendar numbers automatically update dependent on the year, I would greatly appreciate it. Otherwise, I'll just have to manually edit the day numbers each year.

If you have any questions, please don't hesitate to ask.

Chris 😀