Why isn't there a separate field to enter the ultrasound measurement?
Because this calculator resolves everything from a single date, the LMP. To reflect an ultrasound, you work out the adjusted LMP yourself, exam date minus the gestational age it reported, and enter that in place of the original LMP. The formula that runs afterward is identical, only the input date changes.
Is the day shift in the displayed week always equal to the day shift in the adjusted LMP?
Yes, because the week and the EDD both come from the same day count applied to the reference date. A 9-day shift in the adjusted LMP produces exactly 9 days of difference in the EDD and changes the total complete gestational days by the same amount, with no extra correction factor.
Does the displayed gestational age change if I get the exam date wrong, even with the same ultrasound reading?
Yes. The adjusted LMP is calculated by subtracting the reported age from the exam date, so an error of a few days in the exam date carries fully into the new LMP and the resulting EDD. The ultrasound reading alone fixes nothing, it needs the correct exam date to become a reliable adjusted LMP.