You missed some questions, but still this is a good start.
I guess, you're talking about an early rush here, not a late game war. There is a huge difference between the two.
An early game war should just take a few cities while you only have 2-3 cities yourself. A late game war is very different. Your economy should be stable at that point and a war shouldn't hurt that much, except when you get a lot of war weariness.
So if you start an early game war while you only have 2-3 cities yourself and then reduce one enemy from 3 cities to 1, then that's quite ok. Now you've got 4-5 cities and he's got 1. Improve your economy and finish the AI off a little later.
While starting an early game war, you should set limited objectives and when you're starting to run out of troops, then you shouldn't try to take more cities. It will only make you lose your precious troops if you lack the force to do so.
In the early game, your economy can't support a huge civilisation, so you don't want to start an early game war with 5 cities and then capture 3 more. If you've grown to 5 cities, then the enemy has had some time to build units and you won't hold that surprise advantage anymore. Furthermore, your economy can't sustain 5 cities plus 3 captured ones unless you've already developed the technology to do so. But then, we're not talking about an early war anymore.
The enemy can see you and react to it when you do this. It can be a good idea to mass your attack force outside of the AI's range of vision and move it into range just before you declare. That way, it hasn't rearranged its units to counter yours and hasn't had time to build more units.
In early game wars, you want to take the enemy by surprise. Attack it while it hasn't build the force to wage a war. Later in the game, the AI will have build an army. Surprising it while it hasn't build a lot of troops is thus not an option. In this case it's often better to give the first move to the AI.
In your own territory, you have several advantages when fighting the AI:
-You have faster movement due to your roads
-You can heal your troops a lot faster in your own territory and your own cities
-You don't get any war weariness when killing enemies in your territory or when losing some of your troops in your own territory
Of course, you need the stack of troops with which to defeat the enemy stack ready.
After defeating the enemy stack of units, you can relatively safely enter enemy territory.
Early era again. So you still want information for the early rush. I did write something about it in reply to one of your posts in post no
12012.
10-15 base hammers is quite ok for your early game size 5-6 cities. You can't expect a lot more from these tiny things. For an early game rush, you'd want to build such production cities first and go the way of a better economy just after the rush. You don't want to waste time building economy cities which produce a low number of hammers before you start a rush. Of course, high food areas can also be production centres due to slavery whipping.
I haven't seen any blue circles in years, but I don't trust AI city placement skills. But I wasn't really talking about city placement but about city specialisation (although they are related).
Later in the game when you want to start wars, you need quite a lot of units and you don't want to have to choose between building a library/courthouse/bank/marketplace or building a maceman. It's a good idea to have cities with a low commerce output and high hammer output dedicate themselves to unit production (long before the actual war). On the other hand, cities that have a good commerce output but fairly low hammer output could then focus on improving the economy. That way, you're focussing a few cities away from economic improvement but that won't hurt that much as they wouldn't contribute a lot anyway. It also reduces the number of buildings that some cities have to build as the military cities don't need some economic buildings and the other cities don't need the military buildings and won't have to produce units.
City specialisation is mainly determined by the terrain around the city and how you improve it. There are many articles about it in the War Academy.
City specialisation is not a miracle thing, but it does help. Especially when you use the national wonders in well-specialised cities.
Did you patch? I ask because the War Weariness formula has changed a bit in one of the patches. Still War Weariness is not really a problem in early game wars.
Turn off unit recommendations in the options menu (I think, I haven't had it on for long and that was years ago).