Can I drink water before having made Kiddush Shabbos night/morning?
No, it is not permitted to drink water before Kiddush.
It is only permitted to drink water on Shabbos morning before davening, the reason being that before davening the obligation of making Kiddush is not yet incumbent, so that the only problem is eating before davening, which does not apply to water.
However, after davening, and likewise on Friday night when there is an obligation of Kiddush, it is not permitted to drink water.
See Shulchan Aruch, Orach Chaim 271:4; 289:1; 89:3 – and Mishnah Berurah.