You can add "watashi" to every sentence without offending the listener. Adding "anata" (you), however, is likely to be taken as offensive. So, it is better to use the person's name instead of "anata" or omit the subject.
"Are you Japanese?" can be translated as "anata wa nihonjin desuka?", "[THE PERSON's NAME]-san wa nihonjin desuka?", or "Nihonjin desuka?" The first one should be avoided.