Can one daven Drunk and what is the Level of drunkenness that disallows one from Davening?
Preferably one should not do so, though after the fact his tefillah is valid - unless one is so drunk that "he would be unable to talk before a king," and then his tefillah in such a state is invalid. (Shulchan Aruch, Orach Chaim 99:1)
Rema (ibid. :3) comments that "we're not concerned about slight drunkenness" when it comes to present-day wines (which are weaker, either in alcohol content or in viscosity, than Talmudic-era ones) - the more so if one is davening from a siddur. Nevertheless, Pri Megadim says that it's not a proper thing to do.