1) You can get gonorrhea, NGU,
herpes and syphilis. Gonorrhea and NGU are the most common and usually present symptoms in
men.
2) If you were infected then your wife could be infected
3) No, only HIV is passed through breast milk and you were not at risk for HIV
You can get tested for gonorrhea and NGU right now and get a 100% conclusive result. Syphilis takes 6 weeks for a conclusive result and herpes takes 4 months. Without you having symptoms I doubt that you have an STD.