Is it possible to have syphilis without any symptoms or signs? is combo hiv test 4 the generation conclusive at37 days?

Yes and yes: Most cases of syphilis are asymptomatic most of the time. If you think you might have been exposed, you need a blood test. If recently exposed, wait until 6 weeks later. The 4th generation HIV blood tests (also called "combo", "duo", antigen-antibody tests) turn positife within 4 weeks of infection, so a negative result at 37 days is conclusive.