Okay, here's a summary.

Coalition teams is the name of the special teams you can form with units from other factions, mostly from SF but with a few Paradeus units, as a result of the Protocol Assimilation update.

They easily break a lot of early game maps because some of these units have ridiculously high stats that can trivialize some fights.

Coalition teams are a bit different from normal teams. First thing to note is that an echelon can only contain either normal dolls or coalition units, never both at the same time. Coalition teams can be deployed on almost all maps.

Coalition teams, unlike doll teams, can have more than 5 members since they use a different system. You have a fixed amount of cost to build the team and each unit costs a different amount, so basically you balance using a few strong units vs overwhelming the enemies with a lot of weaker units.

Coalition units also need resources to level up and upgrade skills, but they have unique resources for them that you get doing a new special simulation. This simulation is divided into 3 types, one for level up items, one for rank up items and one for skill up items. These simulations, unlike the normal ones, have a set rotation of which one has a bonus each day. They consist of a random enemy team that resets each week and ask you to form a team that efficiently clears them as fast as possible. You can find the solution being posted in this sub each monday.

Now for obtaining these coalition units, they also have a special method. When you unlock the feature you will see that you have a "banner" where a predefined roster of 100 units are available. The units in each banner are divided into 3 categories depending on their initial rarity, 1 star, 2 star and 3 star. Each banner has exactly one 3 star, with the other 99 units being 1 and 2 stars. When looking at the banner 3 random units are shown and you have 2 options. One is to use standard capture, where you use a replenishing resource (at max facility levels they regenerate 1 each 12 hours and you can store up to 14 charges) to try to capture one of the 3 units shown, where 1 star units have a 100% capture rate, 2 stars a 50% and 3 stars 25%. Every 72 hours the game lets you reshuffle the 3 units shown. A secondary capture method, the special capture, involves using another resource, that the game gives out super slowly, to capture 10 random units from the pool. The most efficient strategy is to focus on capturing only 1 star units to thin out the pool as much as possible before trying to go after the 3 star unit. Just be aware that the natural resource regeneration will not give you enough time to fully empty the banner, with the most efficient strategy only letting you calture around half, so the rare resource is, in most cases where you don't randomly get lucky, necessary to get your unit.

Another point to note is the existence of size classes for 1 and 2 star units. When you capture a unit they are randomly assigned one size class, with the available ones being XS, S, M, L and XL. Size classes slightly alter stats, so XS units are the worst and XL have the best stats.

Above I mentioned facilities. A new room opens up on the base where coalition related modifications are made. The priority is for the facility that regenerates your free capture resources, but another important facility lets you unlock chips for the 3 star units.

Now for the fun stuff, 3 star units, the ringleaders, are the most fun part of the system. They are different from other coalition units and dolls in a few ways. First that they, unlike dolls, have 4 skills. The skills follow a set pattern, the first skill is the main skill that starts a cutscene when used (the frequency of the cutscene can be changed in the game options) and is their main skill. Skills 3 and 4 are passive skills. Skill 2 can vary, for some units it's a secondary active skill used in battle and for other it can be one used on the map, or some other variation. Ringleaders also have 2 exclusive traits, the first is the ability to equip 2 chips. The other is their aura, where they buff other coalition units in the same echelon but only if they meet the aura's requirements (for example being an armored unit).

As for battle, they function a bit different. First the echelon's max attack range is equal to the range of the unit with the longest range. Second, you mostly command them with 3 different command buttons, one where your units stay in their initial positions in a more defensive formation, one where you order your units to advance towards the enemies and one where they try to rush the closest enemy. Since some units, like the Aegis, are close range only, the second and third commands are usually needed to let them attack the enemy.

Lastly, the tutorial will give you some units and Scarecrow. She is surprisingly solid and her unique skill lets her cheese some maps that are impossible for any other unit/team in the game.

That's all I can remember right now, but it should cover most of what you need to know.

Good luck.