I’m afraid your suggestion that the S in “use” and the the S in “usually” are the same is false. The S in “use” is pronounced /s/ if it’s a noun, and /z/ if it’s a verb. The S in “usually” is pronounced /ʒ/. The /ʒ/ in English is marginally phonemic — there are no words beginning in the sound, and it’s mostly an allophone of /zj/ (or /sj/), except in a few words borrowed recently from French.
While /z/ and /ʒ/ may be considered similar in English, other languages hear them differently, for example, mixing them up in French will be considered a serious mispronunciation. As far as Standard Chinese, /ʒ/ is not considered to be an allophone (alternate sound with the same meaning) of /z/ or /s/, but is indeed considered an allophone of the Chinese R. Your suggestion of using pinyin Z or j won’t work at all — those sounds (unvoiced affricates) are not even close to /ʒ/ (a voiced fricative).
As far as mixing up L and N, that’s more a feature of southern Chinese (including southern dialects of Mandarin). In any event, it’s probably best for a person learning Chinese to concentrate on mastering the tones.
So, there’s no mysterious rogue teacher — different languages simply have different ideas of which sounds are similar. I hope this helps.
(I used IPA for the pronunciation above)