Civilization – How to find out what cities you already have a trading post in

There's no upper limit on the number of cities you can have in Civ VI. However, your Amenities gained from Luxury Resources can only give a bonus to four cities (six for Aztecs), so every city created beyond the fourth will reduce the Amenities available in each city. Since Amenities impact how productive your cities are you'll want to avoid expanding too fast if the Amenities in your cities are already fairly low.

Other than concerns about Amenities though there really isn't much of a negative to founding more cities, and you'll usually get some benefit from every city you create.

Yes, a Trader can use a foreign Harbour (or a variation thereof) district or a City Centre to transition between sea and land.

However, Trading Posts have nothing to do with this action. Trading posts are not improvements or buildings that civilizations buy, they are established on a per city and per civilization basis. That is, you can have multiple trading posts (one per civilization) in your city.

They are established once a trade route, foreign or domestic, to a city has come to term. They do not cost upkeep but provide bonuses (typically gold) depending on your civilization and civics. They also replenish movement if you move through a city which features one of your trading posts.