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When d or r is placed in between two vowels, their pronunciation is very similar. However, even in the middle of a word, the r retains a bit of a trill that the d always lacks. There is an audible difference between the words todo and toro for example.
You might want to check out this exercise on the D and R between vowels taken from The Complete Guide to Spanish Pronunciation.
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I think by immersion what you really mean is increasing your exposure to the language in its native form, rather than the bite-sized chunks of the language that you get from Duolingo/flashcards/etc.
I started off with Duolingo when I moved to Chile, and I got to right about where you were when I realized I needed something more than just a way to drill vocab one sentence at a time. I actually spent a few hundred dollars on private tutors, but I actually made much better progress using Pimsleur since it allowed me to have more consistent exposure to real conversation.
I suspect that you would get similar results from Pimsleur/Assimil/Michel Thomas or One Month Spanish, although I can only personally speak to Pimsleur and One Month Spanish. I do think listening to podcasts is a great way to create an "immersion" experience, but honestly, you are probably are not ready to jump into podcasts until after completing one of the above.
If you are not so focused on building oral proficiency, then finding a book to read in Spanish is a pretty good next step. The standard recommendation is Harry Potter, which is fine if you like Harry Potter, but I think its better to pick a book that you know fairly well in English (and that you really enjoy). If you like Harry Potter, then great, but my first book was Dune since I had read it at least a half a dozen times in English already. Since I already knew the story so well, if was easy to follow the story even though there were plenty of sections that I simply could not understand at the time.
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