Just to weigh in on the Kiddush Levana discussion:
1. Regarding whether seven days means full or not, and about winter months, see here from Dayan Raskin (will also post pictures below):
https://hebrewbooks.org/pdfpager.aspx?req=30450&st=&pgnum=388https://hebrewbooks.org/pdfpager.aspx?req=30450&st=&pgnum=389In practice, as far as I am aware, this (whether seven days means full or not) is a standing Machlokes amongst Chabad Rabbonim.
[The quote about the Tzemach Tzedek saying “when there may be clouds etc. we don't need to wait 7 full days and 6 plus days is enough” seems to be a misquote. The TT was saying that we could just rely on the Psak in Shulchan Oruch to do it after three days, as per the Shittah of Rabbenu Yonah. I don’t see how any inference could be drawn from the TT whether seven days means complete or incomplete.]
2. Molad is certainly calculated according to Jerusalem time. [As the previous poster mentioned, our modern Jerusalem time does not exactly match the Jerusalem time used to create the Molad cycles. It doesn’t even exactly match solar time there these days, but pretty close to it.] There just is no two ways about it because the lunar conjunction is an astronomical event that happens in one instant worldwide. The same concept is true of the Molad, even though it is just an average cycle of the lunar conjunction, it still represents one instant which is experienced worldwide at the same moment. The time given is Jerusalem time, and it needs to be converted into local time per time zone.
[Some Achronim (see Sefer Aleh Yonah) say that although the Molad is Jerusalem time, that very same time should be used worldwide without converting to local time, because the average person is not familiar with the astronomy behind timezones, and this phenomenon is accessible only to those who are schooled in mathematics and astronomy. To my knowledge, this is not the normative approach. It could also be argued that, these days, this assertion no longer applies, as timezones is a basic given in our day-to-day lives.]
3. Shulchan Oruch paskens that Kiddush Levana calculations, for both begin and end times, are made according to Molad even though it is an average cycle and not the true moment of lunar conjunction. An interesting (debated) exception is when there was a solar eclipse or lunar eclipse that month. A solar eclipse of course happens at the precise moment of lunar conjunction, and a lunar eclipse occurs at the exact time when the moon as its fullest. Since the “evidence is before our eyes”, many Poskim hold, based on the Maharil (Rishon), that we must dispense with the Molad cycle for that month and go with the moment of true lunar conjunction. [See Beis Yosef 426 and Nosei Keilim at length.]