Civilization – see the active diplomatic deals in Civ 6

TL;DR Changes in amenities won't show up until you hit the next turn button.

In Civ 6, each luxury gives you 4 amenities, and extra copies of a particular luxury don't give you more amenities. According to page 50 of the manual:

Only one source of a specific luxury provides amenities, shared with the four neediest cities in your empire.

You don't have precise control over which cities get which amenities, and "neediest" isn't defined anywhere, so I don't know exactly where those amenities are going to go.

In addition, it often takes to UI a long time to update things. In this case, the engine that distributes amenities among your cities only runs after you click end turn, so the UI will definitely not reflect the new one until the next turn.

I don't believe there is any way to see the calculation of the tile yields, but its generally not that hard to figure it out yourself.

There is a handy page here that describes all the details on tile yields, but the general rule of thumb is:

• If it's green it gives more food
• If it's a hill it gives more production
• If it's got some other feature on it then it gets an additional gold/food/production bonus depending on the resource
• If it gives something that is not gold/food/production then its getting a bonus applied from either a natural wonder (always within one tile), a wonder (always in the city), or a religion/pantheon (you can check for this yourself.

That's pretty much all the possible inputs for tile yield calculations.