I don't mind the long banter. Cursed is the person who invented the "TL/DR" shortcut.
So, where is your problem now? Finding them? Figuring out where they are going (course/speed?) Or finally getting the torpedoes on target? Or getting out of dodge when the stuff hits the fans? Obviously we have to try it in that order.
Finding them: Your best sensor on the boat to detect other ships is the hydrophone. Submerged radius is 34km when you listen yourself. If you ask the crew then they won't report anything beyond 20km or so. If they can be bothered at all. That seems quite a distance compared to the visual detection distance with crew on the bridge, 8km or 16km if you use GWX3 or other mods. But when you are out in the Atlantic, you are still sitting on a needlepoint in a haystack. The odds of something being near enough is neigh zero.
Better is to look for icons plotted on the map, clicking on them for details on where they are going, since when and how fast. Personally the range they are drawn around you is rather short, 250km. It's a config file setting, which I personally enlarged to at least 750km. (SilentHunterIII_installfolder\data\Cfg\Contacts.c fg) My reasoning is that BdU sends out these messages that anyone can receive and decode. It is you that determines if you are actually close enough and in a good position to intercept. With the above information I made myself a rule. If the target moves more than 170 km from the initial radio icon then they stray outside of the maximum hydrophone range, and I can no longer be sure they are inside of it. (their given course is N, NNE, NE, ENE, E, etc. plus or minus 11.25 degrees; at 170km this makes an ice-cone with the hydrophone range as the ice ball) If they are slow and I reached inside the 'ice-cone' drawing before they arrived I may have to backtrack them. 9 times out of 10 you find them just late to the party if you made haste with your intercept. They may however changed course in the mean time, so you may loose them on occasion.
Other wise you can try to position yourself in places where traffic merges into choke-points. From there on out you can follow them, get their actual speed and course. Better not do that with ships or convoys inbound for a port. You would have to judge the time until they disappear by de-spawning from the campaign if you can attack them in time. So focus on outgoing instead. Subsequently use the gathered information on them to attack them.
As for tracking, you can do that at a stand off distance. Or sprint ahead like a madman, dive wherever in front of them and do the tracking and final speed and AOB assessments right before you fire. I would say, try the standoff tracking first, as it doesn't get hectic. You'll have plenty of time to get comfortable with learning how to plot, use the map mechanics. Or how to best to manoeuvre your boat.
You can ask the watch officer for ranges and bearings to target on the surface. Mark the spot where you are now. (probably the most hectic part of this) Add the bearing to your current course and subtract any multiples of 360 if you can. Then draw a line on the map from the previously recorded position, in that calculated direction and to the range quoted by the watch officer. Do this several times with multiple minutes apart. 3 minutes 15 seconds as minimal interval is a nice magic number to start with. If you do 4 of those you end up at 13 minutes. And should give a good indication of the path of the target. And the distance between the endpoints of the line (in kilometers) should show a measure of the target speed, 4 times the speed in knots divided by 10. If you want to know, calculate how many meters something at 1 knot moves in 3 minutes, 15 seconds.
If you do the above method, it might however be useful to include some quality of life mods if you don't have them. Stock SH3 doesn't have useful compas-wheels on the cursor tools. So plotting the line isn't as easy. Though you should be able to use the protactor tool to get the angle with reference to north/east/south/west when one leg is exactly horizontal or vertical. I made my own mod, best to enable it with the moding tool JSGME:
https://www.subsim.com/radioroom/dow...o=file&id=3704
I'll await your response to hear if this is part of the journey you are stuck in. Or if it is beyond this point where you get lost.