If you want to make progress, I suggest finding a piece of content 15-30 minutes long, and listening and repeating everyday for a year. Once you have memorized the content word-for-word, then you will be able to stop hearing meaning, and actually hear the sounds.
You could also spend time with a book which explains differences like the 'th' difference in 'thin' and 'then'. I assure you that book will not help you. Many native english speakers don't distinguish between 'pin' and 'pen' but no one confuses 'thin' and 'then'. Trying to learn a bunch of rules will not work. You have to learn to hear the difference, and the only way to learn to hear the difference is to listen to the same thing over and over.
I have an actor friend, who is well-respected professionally. I once discussed how he approaches the new play that he is working on. He said that at first he just rote-learns the play, so that he can keep all of it in his head.Only after that he starts to analyze and think about the role, deeper themes and emotional flows in the play.
I also used a somewhat similar tactic to get better at public presentations. I studied and watched two presentations over and over, making notes about structure, pausing between words, content of the slides, etc. It really helped and I managed to create a presentation that people liked a lot and I was asked to give presentations afterwards in several events.
I have succeeded with the academic approach, I can pronounce English sounds without an accent when I try and with a very slight accent when I don't try (most people can't hear minor mistakes when I speak)
I can tell you the difference between apical and laminal consonants and actually pronounce it. There is not just one way to learn. But I doubt most people can replicate my success without putting in as much time into it as I have. You have to be genuinely interested in linguistics
Once you have learned to mimic one accent you can quickly master another.
Source: I did this myself in Brazil when learning Portuguese. The words that were hard to pronounce I would say like I was from Rio. It was easier to mimic the accent from Rio because it was different from what I was hearing every day. If I were actually in Rio I would have probably found it easier to mimic a Paulistano accent.
I actually have been thinking about something similar for a while too. In my case, I thought that British accent would be easier for me to mimic. I haven't actually tried that out yet and now seems to be a good time to do so. Would British accent be a good goal? Out of curiosity, has there ever been a case of someone having a "too thick" British accent that would make it hard for American to understand?
If you have friendly native speakers, you may be able to get them to exaggerate the sound. E.G. the difference between thin and then is that the 'th' in then gets voiced (your throat vibrates) and the vowel is different. 'World' has an extra syllable (wur - ul - d) vs. 'word' (wur - d). I'm less sure about your issues with the others, save that certain sounds probably don't exist in your native language.
And those you just have to study & practice. I know how hard it is, though, having learned such sounds as 'ng', the 'eu' vowel in 'feu' (French - fire), glottal stops (yes, those exists in the English word bookcase, but...), the Japanese 'R'-group sounds (they're not 'R's or 'L's as we know them).
A slight Southern American accent sometimes does cause many Americans to perceive someone as more trustworthy, and some Americans do find a slight Southern accent to be very attractive. Though, be warned that a Southern accent may cause some Americans to perceive you as more stubborn and slightly less intelligent.
I know, it seems trite. But the point is: think of someone who speaks your native language. Copy their thick accent into the language you are learning.
So when I began to use ze outrrrageous Franch acc-sont, my actual French-speaking improved.