I'm interested in women's roles during the final decades of the empire, especially around the killing of the Janissaries. Would women be moving freely around the city during the time, or did they mostly stay indoors?
They would be moving more or less freely around the city. They would be wearing headdress (although this isn't remarked on in the 19th century), and segregation of the sexes is somewhat stricter, but you would expect to see women in the streets, shopping, visiting relatives, in public parks etc.
Even members of the imperial harem (who were relatively secluded) could take trips into the city under escort.
Source: W. Ball Sultans of Rome