you can't get a night sky in the UK and Australia at one and the same time.
That's irrelevant, as I wasn't referring to simultaneous observations.
. . . the apparent shift in the focal point around which the star constellations appear to rotate at night time in the UK and Australia can easily be understood!
You haven't provided a clear explanation. You just keep mentioning day and night.
There would be a gradual shift of this focal point each 24 or so hours in each region as viewed by an observer in that locale!
There wouldn't be and there isn't such a gradual shift You've already referred to the north star as fixed, not gradually shifting. That applies regardless of how long the night happens to be, provided that the north star is observable. If it becomes observable during the day (due to a solar eclipse), it's still in the expected position, confirming that it hasn't gradually shifted during the day.
This focal point against which star constellations appear to revolve fluctuates from one to the other in varying degrees each day and night!
That's completely untrue (and not mentioned elsewhere, even by other proponents of a flat earth). Also, you've already contradicted it by describing the north star as fixed.