Is one allowed to drink water or any other beverage before Kiddush and Havdala?
After shkiya we are not allowed to drink anything, even water until after kiddush. A woman that is very thirsty, is allowed to drink water, (and according to some even tea), after lighting if it is still before shkiya. The reason why, Kiddush and Havdalah are more stringent than other mitzvos, where we are allowed to eat a little bit beforehand, is because Kiddush and Havdalah are meant to be done specifically at the beginning of the day. Other mitzvos though, although it is proper not to stall it off, and to do it right away, therefore we don’t eat a meal, the time of the mitzva is not specifically “at the beginning of the day”. Therefore, Kiddush and Havdalah are stricter in this aspect than other mitzvos.
Regarding Havdalah, although we can’t drink other drinks, water however is permitted from after shkiya, (unless one is in middle of a seuda). The reason Havdalah is not as stringent as kiddush is because kiddush is on Shabbos, and any eating or drinking on Shabbos is considered prominent, therefore even drinking water is considered prominent and not allowed. By Havdalah, essentially Shabbos is already over, therefore water is permitted.
Kesiva vchasima tova
Kiddush- Shulchan Aruch O:CH 271-4, Minchas Shabbos- Mincha Chadasha 77-2, Shmiras Shabbos Khilchoso 43-46, Piskei Teshuvos 271-12.
Havdalah- O:CH 299-1, M:B 299-1.