"She is asking for some water."
Translation:Она просит воды.
Note that the form вода works as the subject of a sentence, and in this case you need a direct object (the thing she wants, “she” being the subject). So for sure you can't use вода. The alternative would be the accusative, воду, with a different meaning as explained in another comment.
No. Prosit is Latin. It is the 3rd person singular present tense subjunctive form of the verb "prosum, prodesse, profui." Prosit is used today in different countries and in different contexts, for example, drinking toasts. In the context of drinking, it can be translated as "May [it] do [you] good." Prosit!