Looks DIY to me. For the pump you could probably get away with an eheim 1048, or a Sicce Silent 1.0. I personally wouldn't go with a cheaper pump as I don't want to have issues with it. If you could give height and diameter numbers that would help also. If you don't mind spending more there are tons of DC controllable options which you don't need to be so exact with and you can change flow in the future. The eheim is definitely on the low end of flow but it would be fine for a 32gal.
It looks like they didn't give you the other halves if the unions? Fortunately it seems you have 2 different sides so you should be able to buy just 1 union if they are the same size. Also you'll need to plumb the output of the pump up to that top fitting. Tubing is optimal but you could hard plumb it if you'd like.
The black and blue lines are your Co2 inlets. The thing in between is a bubble counter. The red line at the top is the outflow.
To feed my CaRx i use a peristaltic pump because it is incredibly hard/near impossible to use a normal pump. You want something you can dial in to a very low flow made to run continuously. Most dosing pumps don't work for this. The Kamoer FX-STP2 is a perfect fit but it is expensive so I make my own with the $10 pump they have on
Amazon, a 0-12v dial, and a 12v power adaptor. The only issue I have is with the tubing. The stuff that comes with it is cheap and a quality replacement like Tygon designed for peristaltic use or Masterflex can be quite expensive. Even with a higher end pump you need to replace the tubing periodically so it really comes down to how hassle free you want this to be.
The most important and often expensive component is the regulator. You need something with 2 stages that can get down to around 10 psi. I like Co2Art for these as they sell high quality German made regulators for prices much lower than you typically see in this hobby (because they are freshwater focused). Otherwise you could save money here as well by DIY.
For Co2 you want to make sure that you either buy new or if you do the trade in thing make sure you specify food grade as welding and pesticide use can have contamination issues. Because of this I buy new as the local companies who do trade in all charge a premium for food grade.
Lastly for control you can manually dial the thing in but it can be quite difficult and frustrating. Since yours does not have a probe port built in what you're going to need is a effluent box. It is basically just a small chamber (plastic cup even) where the effluent drips into where you can test the ph and alkalinity to set your bubble and drip rate. It also helps to mount the drip tube above the chamber so you can easily count the drip rate without having to hold it in place and this mount could double as a place to secure a pH probe. Even if you don't start with a controller you may want to still include a spot as you'll very likely want to add one in the future. For control you can use an Apex or other similar controller. If you don't have one you can buy a stand alone ph controller and the other component to make this work is a solenoid valve on the co2 regulator. Usually it doesn't cost much more for one that has the solenoid included but if you are sure you will never automate the co2 you can skip it, but there is still utility to using a ph probe so you don't have to manually test ph every time you make a micro adjustment and ph monitoring can let you know when something goes wrong such as a clog, or you run out of co2.
Hope this helps. I know people try to say CaRx aren't that complicated...yeah right.