First, I have to agree with you @shamrockmom Il Nam is one unredeemable character. Wonder If the writer will do anything to make him even a tiny bit useful in this world. I think once he finds out he's a father, he might change. Also, one possible excuse for him seems to be that he couldn't accept Jjang because he has so little to offer. If he gets more financially able, he might be ready to take on responsibilities as a father and husband. He would have gotten together with Jjang if his latest investment hadn't gone belly up.
1. On Jjang. I just wrote the name I hear them calling her. I didn't know it was spelled/sounded ”Trang” in Vietnamese/English until you mentioned it. Jjang is Koreanized word for Trang It seems. Much like how Korean sir names Yi and Bak became anglicized into Lee and Park, respectively. They are not necessarily completely phonetic but much more comprehensible and comfortable for the local tongue sort to speak. I think the same was done in Korean with the Vietnamese name.
2. 김서방/Gim seobang (son-in-law) - JH thanked her because that was the first time SJ’s mother referred to him as 김서방, thereby finally, albeit reluctantly, accepting him as a son-in-law (not 100% since she still doesn't want them to register their marriage). Until then, she’d continued to refer to him by his company title, 김본장, even after they were married, which she would have done the whole time she had known him. Her husband gave her **** for it, but she’d said she couldn't get used to calling him a son-in-law, yet. (Until she kinda felt badly that no one remembered his birthday). This was an affront to him, of course. There is a huge affection gap between being called 김서방 vs 김본장 obviously, especially in Korean, since their culture and language are hyper-sensitive about how people refer to each other. Hope this helps.