I'm in a S-18 with no radar, same as you. I get my firing solution from my plot. By this I mean I must plot myself. It is a lot of work, but pays off in results. I have done plotting both on paper, and on the in-game nav map.
Radar is certainly a powerful tool, but you can sink ships without it.
As far as the attack map is concerned, I can't tell you much about it as I never use it. I gather its usefulness is limited to graphically showing elements related to the TDC. I don't use it since I'm not using the TDC and I can't make any marks or lines on it anyway.
I think you should keep your scope up until you get a contact. If your crew cannot see anything, then you don't need to worry about your scope being spotted. You should not rely on sonar alone. When I'm cruising submerged, I will set my depth to 45 ft. or even 40 if seas are rough, and leave the scope up. In RL, captains wanted to keep their scopes as high as possible to search the maximum area. Of course, when a ship is at a tactical distance, I go back down to 50', and keep scope exposures short. At long range it is almost impossible to spot a periscope.
In RFB, there is no way to track torpedos on the map, but if you have time, you can pick them up on your hydrophones.
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