I've never played older Sid Meier games, I only have experience with Civilization 4 and 5, so the control scheme in this feels awkward, and neither the tutorial or the manual does a stellar job of explaining them. So could someone give me a basic rundown on unit control, as well as Civ and city management? Thanks.

There is no control scheme. It is a civilization game.

Most of the stuff on the screen is irrelevant unless for some reason you wanted to know exactly how much of a resource you are taking in/using, which there is not generally any reason to know, except sometimes energy. On the right you have units that the city is supporting. Different social engineering choices can pay for units without taking minerals. if it is using a mineral it has a little red dot.
On the left is the production selection screen.

The game will tell you if you have drones or starvation, the latter which only occurs if you are dumb and turn all your farms into forests.

It is identical to the civilization series in that it has no real management. You flexibly make things in the right order for success.

You can solve drones with the recreation facility you can get from the "build "research path. You can build the Virtual Reality project to turn your network nodes into Hologram theaters.
The human genome project will create one talent, which will help you balance out against your drones to prevent drone riots. It is less useful than Virtual Reality. These two projects are on the discover research path. Peacekeepers get free talents.
You can put funding into pscyh in the social engineering screen. I almost never use this.
Efficiency can increase the number of cities you can make before you get drones. I don't imagine this latter option is particularly useful, but I only play Yang, so I have no efficiency rating or real drone problems. Ultimately you can just turn your workers into specialists, which will solve drone problems.

I don't know what you don't understand in regards units. It has a menu. You don't need to use the menu, the only thing you can do with units besides more or attack is SHIFT+H or spacebar. You use the hotkeys to control your formers. f, shift+f, s, r. It is straightforward. You get more terraforming options with Weather Paradigm, and makes terraforming slightly faster, but the boreholes don't work until you have research.

You can find the faction stats under help>index>faction profiles. Every faction has a favored engineering choice in regards diplomacy which should be somewhat evident if you don't want to go into the faction editor in the games folder.

As for older Civilization games, I hope that GOG gets Civ 3 along with it's fantastic manual. Consider voting for Civ 3.

I can see how unit control could seem a little wonky at first glance; unlike Civ4 and 5 where you can move units with a simple right click in Alpha Centauri the most common way to move units is to left click on the unit then drag the mouse to where you want the unit to move (a green line will appear indicating the path the unit will take). There's also much less of a GUI for controlling unit actions. If you right-click on a unit a menu of unit actions will come up that you can choose from, but there are also hot-keys for all unit actions and it's recommended to learn at least the common ones as it makes playing the game a lot easier and faster.

For city management, there are three resources you need to worry about, just like the other Civ games- minerals (production), nutrients (food), and energy (money). Just like the other Civ games you can improve the areas around your cities (terraforming) to improve resource output, although there are quite a few additional improvement options than the other Civ games have (and you can have multiple types of improvements per tile if the terrain allows for it and the improvements are compatible). Something a little bit different from the later Civ games is the unit upkeep is managed on a per-city basis; units a city is supporting is shown in the lower right of the city screen. You'll want to keep an eye on this, as early in the game having one city crank out a bunch of units can quickly kill that city's production. For managing your citizens there are three types of citizens- regular citizens, talents, and drones (and any citizens that aren't working tiles can be various types of specialists). Drones are unhappy citizens, while talents can basically be viewed as extra-happy citizens. If the number of drones in a city becomes greater than the number of talents then drone riots will occur and the city will basically shut down until you end the drone riots (most easily done by re-assigning some citizens to be specialists). There are various city buildings that increase the number of specialists and decrease the number of drones that you'll be able to build.

For civilization management you have research, diplomacy, and overall civilization income like the other Civ games. Research can be a little bit different as you're not shown an overall tech tree, but rather just given the option to choose between research goals from time to time (there's also a setting at the beginning of each game that can make it so you can only choose general research direction rather than specific goals). There's also social engineering which is basically like the civics in the Civ games. Something rather different from the Civ games is the workshop, which allows you to design your own units based on available technology. The game will automatically design plenty of units as you discover technology, but you can also create customized units if you feel so inclined.

There's plenty more to the game, but that should at least give you enough of the basics to get started. Most of the options in the game are hidden in menus, so I'd recommend poking around when you first start to get a feel for what all is available and where it's all located.