1) 힘들다 vs 어렵다 Basically 힘들다 means demanding a lot of energy, power, competency etc. 어렵다 means difficult. Let's say you are trying to move 100 bottles of water. That is not a difficult job, but time, energy- consuming job, so we can use 힘들다. But, if we are talking about solving a math problem, 어렵다 (difficult) would be better combination. But sometimes we Koreans use those two words interchangeably... unconsciously. 2) 풀다 vs 해결하다. 풀다 literally means untie, unleash, untangle, solve etc. 해결하다 usually means solve. Simply speaking 풀다 has more meanings than 해결하다 does. Then, in case that both two words means solve, still there is a subtle difference. 해결하다 sounds more formal than 풀다, because 해결하다 came from 解决. Usually the Korean words from Chinese sound more formal than pure Korean words, just like some Greek or Latin - originated English words sound so.

1) 여전히 = 如前히 = like before, still 2) 아직(도) = yet Roughly speaking we can say 여전히=아직도=still, but some interogative or negative sentences , where you are generally use 아직도(=yet) rather than 여전히 (=still), there are some very subtle differences.

"ㄹ" is just one of Korean alphabet characters, so it itself doesn't have to do with good or bad pronunciation. I've heard Korean "ㄹ" is pretty much close to the dark "L" sound in American English, like in "milk", but the exact sound would be different. You can not but repeat native Koreans to master its pronunciation.

Yes, I think you guess right :). Or the equivalent in English is tag qeustions. So, "거기 재민씨 집이지요? = Is this Jae-Min's residence, isn't it?" BTW, you have to omit "에" in your original Korean sentence "재민씨에"

I don't exactly understand your question, but FYI... 60% of the modern Korean language's vocabulary are from ancient Chinese (just for your information, some Korean scholars claim that at that time we Koreans invented Chinese chracters, so Chinse character is not a correct word but Oriental character is more proper word), and those can be written in Chinese character even today, albeit we Koreans usually just use Korean pronunciation letter of those Chinese character. And Chinse chatacter is so meaning-condensed hieroglypic that you would need to use more than 2 words when you translate it into English.

just like in English, you don't need to repeat "receive" when you answer, except that you are intentionally put emphasis the very action of "rececing." But, unlike in English, anwering without "이다 (to be)" is usually considered being rude or childlike, but still depending on the exact situation. And, I think which variety of "이다" - i.e. 에요/입니다 - you would choose is sort of idosyncratic depending on who you are answering to, albeit "-에요" is more common and sounding naturual in colloquial dialogue.