If I understand your system and questions you have OpenCPN functioning correctly with data from your Garmin GPS. You want to use a Serial DTECH Communications Data Converter Adapter to get data from OpenCPN to the AP.
I'll tackle the "easy" part first. Sending AP data from OpenCPN. Open Settings/Connections/Add Connection and set up a new connection. Some of the setup is simple, some not. Here's a full discussion
Route to Autopilot OpenCPN The most challenging part for me has always been getting the data port correct. Sorry, can't help with that, it's going to be system dependent. Consult your AP manual to see which NMEA sentences it needs to function.
Next the hardware. There will be two connections to make. The first is Mac Mini to the converter. Then converter to AP. I can't help with Mac Mini to the converter because I don't know diddly about the Mac Mini.
From the converter to the AP is sort of straight forward. I'd first try RS422 because most older NMEA 0183 devices use that protocol. Your AP manual should tell you where to connect the two wires from the converter. It should also tell you the serial protocol so you know for certain if RS422 is needed. Remember when you test this the two serial data wires are polarity sensitive. There is no risk to the equipment getting the reversed but it won't work. There are a number of good resources on the net on how to troubleshoot and test NMEA 0183 data. This link
Testing NMEA0183 might be a good place for you to start. The author describes a simple test using an LED to determine if there is a live connection and if polarity is correct. I've used this in the past with good success.
If you are not successful at this point one you may want to "see" the data coming into the AP. This is going to require additional hardware and software. Something that you can connect to the two wires you would normally connect to the AP and view the NMEA sentences. But that's another NMEA / serial data nightmare in itself. However here's a link to a good discussion on
NMEA 0183 sentences. You don't need to read the whole thing. You'll be looking for lines of text that start with $ and then a 3 character sentence description then the data. If you see the sentences the AP needs and recognizable alpha numeric characters then all is probably good. If you see garbage then certainly it is not good and you need to check all of your connections. To get an idea of what a healthy NMEA sentence looks like with OpenCPN running and recieving data from the GPS open Settings/Connections and tick the Show NMEA Debug Window box. A stream of proper NMEA sentences will display.
You've set yourself a challenge. Connecting new to old to really old tech. It can be done but and you'll learn a lot in the process.