I dunno, I would personally never go for hammer trade routes, as the return is pretty bad. Rather just food grow that city so that more tiles can be worked to make up the deficit. As a last result, at least the unemployed citizen can contribute to hammer. Every cities should have some mines, if there are none, don't bother planting a city there anyway. You have to work a certain number of production tiles. If there aren't production tiles, even if you can rush buy workshop there, the city will still be behind as it's not going to support renaissance buildings without rush buys. If you're playing tradition at a high enough difficulty, it doesn't matter as long as you can rush buy science buildings, the city doesn't need to build anything else. In some of my games, I had cities that don't build anything meaningful until I discovered Coal/Oil during industrial era.
I think we'll have to agree to disagree on this one. I don't think having multiple mines are entirely a necessity. As long as there is 1-2 although I'm not talking about the capital, a city such as this can probably be placed last when you have more trade-routes to speed it along.
Regardless a city working jungle will be a mid-game powerhouse in science in gold.
If I have a poor production city that produces 10 hammers per turn it will take me 16 turns to build a University.
If I route 2 cargo ships with hammers to it I'm getting about 26 hammers per turn and I'll have my university built in 7 turns. This means I'll be able to work those specialists 9 turns earlier which will grant me an extra 54 GS points. So it certainly does make a difference.
Once your universities and a few other essential buildings are up switch the cargo ships to food or other jobs and let the city work all the science from the jungle.