EBEFL asks 4: desperately seeking theory

I’m looking for your help with theory. Here are a few language learning incidences that have happened to me and I’m curious if anyone can associate any theory with what happened or can explain what was going on, or let me know if you had any similar experiences.

situation 1
I was in a shop in Taiwan and the woman serving me told me there was a ‘zhekou‘. I’d never heard this word before but I guessed (from context!!!) it meant discount. A few minutes later a friend confirmed that Zhekou was in fact a ‘discount’. I don’t think I ever encountered that word before and yet I learnt it instantly and never forgot it. 

Situation 2
I was one taking a Chinese class and said the word ‘duo’ meaning ‘a lot’. I got the tone wrong and the tutor correct it with a recast. I nodded a thanks. I never got the tone of that word wrong again and almost every time I say it I can picture the tutor saying it. Is there an explanation for this ‘insta-correction’ and how effective it was? 

Situation 3
I kept hearing the word ‘kichin to’ on Japanese TV. I could use it in a sentence and knew that it generally came before a verb, but had no idea what it meant. I asked someone and it means something like ‘properly’ (do something properly/completely).  I could use this word correctly but didn’t know what it meant. So what’s going on here? 

Situation 4
I learnt the phrase “n ja nakatta” (東京に行くんじゃなかった) after living in Japan for a while and being able to speak Japanese fairly well. I don’t remember hearing it before that but it seemed like absolutely everyone was using it after I learnt it. Is this just a case of recency illusion or is it a specific known thing in language learning?