Sure, NC earlier is better, but give yourself all due credit! T110 NC is really slow for Acken and the other great players. It is more than fast enough to have a strong game.
Just dipping once into negative happiness wont kill your game, and -7 is not much different than -1. Being at -1 for 20+ turns is a problem.
Micro managing tiles is harder than it looks. Compare what you think is good to what the default governor thinks is good, including how many turns for the city to grow. At launch, the governor did a terrible job picking tiles / specialists. And some people can't stand losing one hammer every time the city grows. But it is very easy to sabotage your game by locking tiles. I strongly recommend you give that up for now, and spend your time and energy on other game aspects. Like not losing cities/units when fighting at 2:1 odds.
Gold to upgrade archers to CBs is something I also struggle with. Especially against the conventional wisdom to rush buy all your science buildings. CBs are sooo much stronger than archers though. 3 archers against a T112 hoard would not be enough. 3 CBs should be fine.
Yes, ranged units behind the city so they are safely screened. That is 4 shots a turn, 2 elephants dying every turn. Your city will end the conflict in the red, but it will last 3 turns. Then you start marching your veterans towards Carthage...