Now I am playing as the zulu and so far I managed to take around 4 american cities and I razed one when france tried to build close to me. I am just sorting out my troops and I got around 1 compo bowman, 2 catapults, 2 swordsman and a spearman. One of my biggest mistake was I forgot to build a barracks (forgot the name of the zulu UB). I think its a great progress for me since I increased the difficulty to prince.
I feel like I am doing a lot of things wrong in the way I play however I can't see the things I have done wrong as of the moment. As for worker automation, I either manual or kill off the unneeded worker. I just have problems at times on how to use my workers wisely especially when there are tiles to improve but my city does not have enough people to work on it yet. One other thing that confuses me is whether I should follow the advisors when it comes to research, buildings and other stuff?
I am starting to make a habit of turning on the yield icons even though it crowds the map since I think in this game I have been placing more effective cities. Aside from the resources I want to get, how do I determine which tile is a best tile for a city?
the advisors!
You should be playing with all yield icons + grid. It would be rather awkward not to. (I remember that after I finally found out about those I immediately improved my game tons.)
Luxuries are not as important as you might think (you should still improve them of course, but then sell them as actually the early happiness is even bad for you - delaying the first golden age until you actually have some gold/production/culture going is a good strategy). Early on you should farm all the tiles next to fresh water (I guess they all show as flood plains if i'm not mistaken) and usually get Civil Service asap. Food is generally the most important thing in this game and you can't go wrong with many farms, however boring it might seem. That wasn't the case in Alpha Centauri where forests were a good option, but here you should only build the occasional lumber mill if it you already have a significant food surplus (or are playing a specific forest-friendly civ) and the 1-2 production bonus won't be too insignificant. For this very reason the best wonders to go after are The Hanging Gardens and Petra as those are the only ones that give you food bonuses (and Petra is just too damn awesome on general principles) and they're not targeted by the AI or even by most human players.
If you don't focus on food early you might just forget about specialists and this is generally not a good thing and not very fun anyway.
The main exception to the rule is your main coastal city which benefits greatly from 1-3 manufactories asap as it gets 2+ food from each water tile, but no production, and having no palace to speed things up means that you really need the production bonus.
I have one advice that goes against general principles as far as Civ games go. Don't assume that mass expanding is so good by default. This game has employed huge detriments to expansion - you have -3 production/gold/culture in your expansions, so they are much less useful than your capital early on and the incredible penalty to your policies is not worth it. In fact I'd advice most players to learn how to patiently stay on one city and tech (going tradition ofc) until they are completely sure what the best expo would be. And it turns out the best expo is very often a coastal city state and those tend to wait patiently for you to get them while building the buildings which you'd need anyway. 2 very tall cities and a defensive/diplomatic game with a focus on allying a lot of city states is a good strategy that will help you learn the mechanics, the diplomatics and late game mechanics. Still, you'd usually have to go to war to get 1-2 annoying cities out of your close proximity and possibly negotiate a good peace treaty deal after you've pushed your enemy back.
And after you learn that learning to play with more agressive civilizations is in order, but I'd still advice against having more than 3 or at most 4 real cities (as opposed to puppeted). Either puppet ot raze your way forward. It turns out that not all additional cities are a benefit. More often than not they can be a detriment lagging your policies and happiness and stretching you out too thin.
And finally - winning a diplomatic victory is easier than you might think even on higher difficulties. The AI doesn't seem to be prepared at all with how to deal with that. So keep your spies at work, do the city quests, spread your religion and vote yourself to victory at emperor. (and probably nuking the hell out of your annoying neighbours on general principle while you're waiting for it) I haven't played much at immortal yet, but I suspect it's not too different there anyway.