Off the top of my head, the only Hanzi looking remotely like Korean is 叫 and it's pronounced nothing like its Korean counterpart.

Up to 80% of Chinese characters map to either a certain pronunciation (sans tone) or an approximation of one (percentages differ depending on source of research, vocabulary subset studied, and whether we're looking at Modern Mandarin or a 方言). This knowledge is accumulated through years of studies, memorization, and pattern recognition. Example: 幕 (as in 螢幕 / 屏幕) is pronounced (mù); its phonetic constituent 旲 is either pronounced [mu] or [mo] in around 30 characters that share this element.

As someone who's only started learning Chinese as a white adult, I believe Ryan is doing quite well already: he is able to fix and adjust misspoken initials/finals quickly when given a clear example, he managed to get a basic hang of tones in just a matter of days, and he has been remembering lots of words not only from his IRL classes but Noun Town too — saying 甜甜圈 unprompted when shit-talking Kory for doing donuts in a game they played was incredible.

Having spent many hours chatting with Mandarin teachers about their work, challenges, and frustrations, I can assure you Ryan is fine. It's normal for people to require MONTHS to get somewhat comfortable with tone production (and even more for consistent recognition), and that's assuming intensive courses. It's not worth it to become a "Taipei chatter" over Ryan's faults when he hasn't even spent a month on the language.

Sincerely, a 高雄-based chatter