How to translate "干妈","干爸/义父","干儿子/义子“?
The concept of 乾媽 and 乾爹 in Chinese culture is almost the same as " godmother and godfather in Western countries. To become official 乾媽 and 乾兒子, there has to be a rite or ceremony performed in front of witnesses. The relationship is formed in the name of gods, and is acceptable to everyone else.

However, in modern days, people tread the relationship of 乾媽 / 乾爹 and 乾兒子 much more casually, any close friend of the family can become an honorary mother to you just by oral agreement between the parties involved ( you and your 乾媽 or your parent and your 乾媽) 

In your case, the most appropriate way to describe your 乾媽 in English, would be "close family friend". The visa officer would then understand you are not related to her, but she could be seen as a non-blood related authority figure to you. 

The fact is. The visa officer just needs some probable reference from someone who can vouch for you. That person needs to be a citizen in good standing, know you and your history intimately. A " family friend" suggested just that.


  P.S. I need to write an "invitation" letter to her, and I am trying to fill this blank at the very beginning: Dear ______,


In this case, just a simple "Dear Aunt + (her first name)" would do. 

If you want to be less formal, you could use "Aunty"

Just like in Chinese, "aunt" in English can be used to address a female friend of your parents, or addressing your friends' mother.  

In Western culture, there's no special term for addressing one's own godmother. You don't hear people saying something like: " Hi, Godmother Sally!" (or whatever her name is) People just call their godmothers by name, or "aunt + (her first name)" presuming she is also a friend of your parents or a mother of your friend