My info on syphilis is limited but here are my best answers
1. Dr's on this site often say 6 weeks is conclusive
2. I am sure it is possile but probably unlikely because if anything it would have a possibility to cure it. I say 6 weeks is still valid
3. Diagnosed is easy from a throat swab, but oral gonorrhea is uncommon and oral syphilis is even more uncommon.
I would not worry about either.