I used 1/8" port size and 12VDC for the soleniod. If you are using Apex you need to figure out what voltage(s) are available. If I recall correctly you have a 24VDC line. You can also use 120VAC (line voltage) and plug into a socket. I don't recommend using a soleniod with line voltage because the voltage conversion creates a lot of heat and that usually means a limited life for the soleniod. I could be wrong about this there is a soleniod that people use that build high end regulators. There is a thread here on R2R (you will have to search) the other thread is on Reef Central. For clarification I chose 1/8" so I could get the nice air tube adapters. Here are all of the links:
https://www.ebay.com/itm/121146805630?ssPageName=STRK:MEBIDX:IT&_trksid=p2060353.m2749.l2649
https://www.ebay.com/itm/162445022006?ssPageName=STRK:MEBIDX:IT&_trksid=p2060353.m2749.l2649
https://reefcentral.com/forums/showthread.php?t=2461771&highlight=Leak+test
I would use a doser that doses specific amounts at specfic intervals. I just use the Kamoer cheapy. Also the dosing pump should be plenty strong enough to not have to put pressure behind the doser. Having pressure like this will make the doser inconsistent. You don't want this. My configuration is to pull from the tank and then push through the CaRx. I then calibrate the doser from the line that goes back into the tank (or in your case the sump). That way I can have a reasonable idea of what my flow is. It isn't important that you know the exact amount just that the flow is consistent. This is the doser I use. If you need more horse power the DOS might be a good option for you.
https://www.bulkreefsupply.com/x1-bluetooth-micropump-kamoer.html
Here is what I would do. Get a glass of water and adjust your CO2 so that you have a consitent bubble rate. Do this without the soleniod on. You just want to get your pressure regulator down low and get your needle valve about half way. It isn't important what the bubble rate is just that it isn't bubbling like mad. Like I said mine is pretty high. The problem that I found is if you try to get a very low bubble count like 4 bubbles per minute then the needle valve will drift down (no clue why) and you will end up with no bubbles. One to five bubbles per second is not unreasonable, but might be a bit low. Once again it isn't important the amount just the consistency. Once you get this in a glass and you know what it is. Then you can get a rough idea of of how many bubbles per second that you get.
Now hook up your soleniod and set it up on the controller. Figure out what your lowest on off time is. My guess is it will be like 1 second maybe even up to five seconds. Once again it doesn't matter. Ok, now that you have everything set up. Set up your off time to something high like 15 minutes, so on for 1 second (or whatever) off for 15 minutes. Now it is time to cycle the soleniod. Have your controller start. Make sure you are watching the bubble count. It will turn on, bubbles will come out, it will turn off. Bubbles will still come out. Count the bubbles until they stop. This will give you a rough idea of how many bubbles per on cycle. Just remember the shorter the on cycle the tail end of the bubbles might get wiped away with the next cycle. This is just a way if you know your bubble count to roughly match it or if you have calculations to match them.
Now that you have the bubbles set up you can switch back to your doser. This is the super easy part. Just set you effluent rate to something. If you have a probe this can help to get these two to line up, but I DO NOT recommend probes for anything other than this. Also you don't need the probe it just brings some of the guess work down. If you don't have a probe just set the effluent pretty high and the bubble count low.