If I visit a synagogue, what are the do’s/dont’s?

im a goy/gentile, and my country has a Jewish population of abt 115,000 (maybe..? mostly in melbourne and sydney) and im really interested by judaism as a whole

i wanna visit a synagogue out of curiosity, but what are the biggest no-nos i should be wary of? (and do a lot of synagogues typically have male/female separation i think called mechitza, or is that like depending, cus i would know not to go into the male part)