How long after exposure the rpr syphilis testing is conclusive? is 6 week enough to conclusive? does syphilis easy to die outside the body? or easy to die after you wash the contaminated object with tap water?

Probably there was no risk from the "contaminated object", unless it was a dildo or similar object that had been inside the vagina or rectum of someone else within the previous minute or two. Even in that situation, the water rinse would have eliminated any risk. A negative RPR at 6 weeks is conclusive.

Within the capability of the test done- yes it is conclusive. The syphylis bacteria dies in several hours when outside when washed away. from an object