I can give an answer to this in regards to European cities during the 16th and 17th centuries. I know that's not quite what you asked for, but it's been a day and there aren't any answers; if the moderators decide to remove this I completely understand.

It would not have been common practice for people to present a pass at the city gates. As you suggested, the large number of people going in and out would have impractical to control in such a manner, particularly on market days. 16th-century Antwerp held a weekly 'free' market, for people who lived outside the city to come and sell their goods within the city walls. On such a day, you wouldn't have had much difficulty getting into the city without notice, particularly if you looked like you were selling something.

However, guards could still stop you and ask you questions, and it was at their discretion to let you in. Being foreign, generally unusual, or looking like a vagrant, could land you in hot water. Having an address you were expected at would have been a great help if you were stopped at the city gates. For example, in 1650, when the Royalist Richard Fanshawe and his wife Ann were attempting to get into Galway to catch a ship to Malaga, the guards only permitted them into the city because they could give the address of a wealthy merchant who they would be staying with until the boat left the harbour. They would have stood out to the guards - they were English people in Ireland, their clothes marking them out as Royalists at a time when the country was largely under Parliamentarian control, attempting to get into a town that was still fighting off the last of a plague breakout.

I'll also add that attempting to get into a city after dark, even via the gate, would have been considered suspicious. In a world with no electric lighting, night can be dangerous, and city gates shut accordingly. 16th-century Antwerp's evening bell that signalled the closure of the city gates was called the diefclocke, or 'thief bell' and is a good indication of who was considered to be sneaking around at night.

If you were attempting to bluff your way into a city, it would have been good to know about its provisions for merchants, as they sometimes had community houses. For example, in 16th-century Antwerp there was the English House. It was a centre for English traders in the city, a well-known place to eat, stay, and socialise - and it could serve as your address in the city. The English priest William Tyndale (1494-1536) ran away to Antwerp whilst producing bibles in English to be smuggled back home, and used the English House as his address for post/mail. If a guard stopped you at the gates, claiming to be a down-on-your-luck foreigner headed for your relevant community house might just do the trick.

In regards to your bonus question: not really. For this we can look at Chapter 8 of Simon Schama's The Embarrassment of Riches, which deals with the concept of being an insider or an outsider. Schama tells us that people of all social classes exist on wealthy streets in 17th-century Amsterdam. There are several paintings by Jacob Ochtervelt from the 1660s which show working class people in the entryways of rich houses, selling grapes/fish or performing music for the lady of the house. Paintings from the time also suggest the presence of beggars in wealthy neighbourhoods. Ochtervelt has a painting of a rich woman giving alms to a poor woman who has come knocking on her door, and Schama discusses at length the painting The Burgher of Delft and his Daughter (Jan Steen, 1655), in which a wealthy man sitting outside his house considers the plight of the woman begging at his front step. However, if the cry goes up from a rich house that there's been a burglary, and you're not obviously wealthy, you might find yourself in a tight corner.

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This answer is based on:

L. Moore, Lady Fanshawe's Receipt Book, (Atlantic Books, 2017)

M. Pye, Antwerp: The Glory Years, (Allen Lane, 2021)

S. Schama, The Embarrassment of Riches, (Collins, 1987)