Here's the offending sentence:
I studied English by doing X, Y, and Z ... Then my English improved."Then" indicates that something follows something else in a SEQUENCE, and that's not wrong here. But "so" indicates that something is REASON or CAUSE of something else.
Most people would agree that studying is the cause of improved English skills, so "so" is more accurate here: "I did X, Y, and Z ... So my English improved."
I've got free time later this week, so I'll blog more mistakes. I will tell you the next blog topic in advance. See if you can straighten out this sentence: "She was complained about staying up late at night by her roommate."
Please use English well!