I don't really understand which joint you are concerned about water being trapped at. If it is a glued joint then it should be no problem.
As for the questions on the brass... the finer threads on the brass tube/pipe are for screwing into the tee or drain. The larger threads on the outside of the tee are for metal or plastic compression nuts which would have either a rubber washer or beveled nylon washer. Where brass is screwed into brass these nuts are not necessary and I would only use the pipe thread compound/dope. Teflon tape is the choice of alot of people but on metal to metal I prefer the dope. It acts as a thread sealer as well as a lubricant when assembling parts.
if you are making your own P-trap... is it possible to extend the fixture end with a piece of pvc pipe and trap adapter to be higher than the effluent end?