@manderlay- Good morning and welcome to Mayo Connect. Your English is very good. I can not imagine how difficult it must be to see your dad so ill and he's lucky to have you doing some research for him. I am a lung cancer survivor and your dad's cough is very common for people with lung cancer with or without blood. I had blood when I coughed. I think that after 3 weeks that the cough from smoking should pretty much be gone, but I'm not sure. Maybe your dad feels a trickle in his throat that makes him cough. Sometimes heart conditions can cause coughing. You might want to look that up as to why that happens. He could also have some post-nasal drip that is causing this, or a combination of them. And some medicines can cause coughing. It's so difficult to know or pinpoint what type of cough it is and from what but since he has lung cancer I would place my bet on that. There are lots of meds to help calm coughing but your dad's oncologist should be the person to prescribe something because he will know which meds won't interfere with his chemo.
It's very important that he drink lots of water to help rid his body of chemicals and help keep his mucus from getting thick. Is your dad having any pain? Other than the cough does he have any other symptoms? It's very good news that your dad has no metastasis in other organs. Do the doctors know why there is fluid around his heart?