Additional condition: at least one surplus food sheaf in center box (Food Bin on the right does not matter). Also, Aquaduct and Sewers are necessary to grow beyond 8 and 12 respectively (ie- "celebration growth" does not supercede normal growth limitations).
Mardukes:
Yes, one of the powers of alliances is that you can freely move any of your units through the ally's city radii, which means you can bring in settlers or engineers to help improve their terrain. This will help them grow, if you have given them the happiness and growth techs that they will need to keep it under control. The AI does not prioritize trade in selecting and developing its city terrain, so if you want bigger trade routes you should consider help them along with extra roads and irrigation, if you can spare the workers from work on your own SSC.
One of the first goals of exploration is to find out if you are alone on your continent. Many players consider another civ on their continent a "him or me" situation and focus all their efforts on wiping them out. But if you look at things from the viewpoint of trade, having another civ on your home continent is a God-send, if you can find a good spot for your SSC there. Getting three early trade routes to an AI city on your continent, getting an early alliance with them, and building a "critical path" road between the SSC and the AI trade route city (or cities, but one is usually easier and quicker) will set up huge trade routes that boost your SSC research into the thousands. I am currently playing with a One City Challenge that has three +40 trade routes (city size 25, only one tile not contributing trade (a Mountain I am cutting down), got Colossus and SuperHighways) with an AI city that is only size 8, but I quickly added the "critical path" RR link once I got RR. The multiplication factor of the SSC's science Wonders is what makes this so powerful. Also, the early commodities that got locked in for those trade routes will often change as the city grows, so the SSC can then produce and deliver unlimited numbers of caravans overseas (NOT to the AI trade route city!) for huge delivery bonuses. My city has Gold, Oil, and Gems unblocked and repeating, while my early locked-in trade routes are Hides, Silk, and Wool.
You cannot make the AI build specific improvements like Aquaduct or Superhighways in their city, unfortunately. But if the food is there they will often do the right thing to increase the city size, eventually. The AI tends to focus early terrain improvements on irrigating Plains, while leaving shielded grass alone. Move one or two of your own workers up there to road and irrigate their grasslands and you will see them grow quicker and have more trade arrows to increase your trade routes. Keep the alliance at all costs, avoiding meeting with them unless their Attitude drops below Cordial but giving them anything they demand. Try to avoid making peace with anyone they are at war with, because that will be an issue with them. If you lose the alliance, any of their units parked on the "critical path" road/rail line will lower the trade route value.
As for the fortified trucks, just makes sense to fortify anything you have in the city that is just waiting there. I don't see a City Wall, which would make fortification meaningless.