Question (Part A): Is it ever the first day of the new lunar month (NMD), and yet, a short distance away, under the SAME SUNRISE, it is only the 30th of the old month?
Answer: No. This is not possible - if DAWN occurs at precisely the same time for both locations. If, however, there is even a slight difference (even as little as a minute) in the DAWN times, the proposed scenario is possible. Bear in mind that the Luni-solar calendar uses the first DAWN after conjunction [not SUNRISE which comes later] as the start of New Moon Day [NMD].
Question (Part B): Shouldn't the entire earth be united in keeping the same daytime/daylit DATE in the SAME 360 degree/24hour circuit of the sun?
Answer: The entire world IS united in observing the feast days [in the Luni-solar calendar] – all beginning within the same 24 hours. Looking at question A. above for example... If location A begins New Moon Day, [the first of the new month] while location B is observing the 30th day of the [expiring current month], location B will begin New Moon Day when the sun makes it back around to them – all within the same 24-hour period that commenced when location A began New Moon Day. It can be a lot to wrap one's mind around. It's the man-made IDL (International Date Line), though, that is really causing the confusion.
Question (Part C): Why can't the whole world celebrate the enitre feast (beginning to end) on the same daytime date, all encompassed during the same 24-hour revolution of the sun?
Those on the dark side of the flat earth will not begin their day until the sunlight reaches them. After they begin their day, it will be 24 more hours before the sun returns back to them - at which time, they will begin a new day. Not everyone begins their day at the same time; consequently, not everyone ends their day at the same time. This is true even for the man-made international date line adherents. Everyone BEGINS their day within the same 24 hour period, but the entire world is never observing the same "day" at the same time (e.g., It is never m-nday everywhere on earth at the same time.). The only way the entire world could observe the exact same 24-hour period is if every location had exactly the same starting point for the 24-hour count; in order to achieve this, you must demand that everyone start their day at the same precise moment - regardless of where the sun is in relation to their location. That is to say, if we start the 24-hour count at dawn on the east coast of the United States, Australia and Asia must begin their day at that same precise moment - even though it is dark there. The day begins at DAWN; consequently, different locations have different starting times for their days. Different starting times means different ending times (and the time between the starting time and ending time is always 24 hours). It is always the case that... Some locations are beginning a new day while others are still experiencing the night time hours of the previous day. Using the "dawn after conjunction" method of reckoning, every single location begins their day within the same 24-hour period. It is utterly impossible for the entire world to both begin and end their day at exactly the same time - unless you insist on arbitrarily deciding on a starting time and then force everyone to begin their day at that precise moment (regardless of whether it's morning, noon, afternoon, evening, or nighttime in their location).