In the English language, you can refer to you mother as "mother" or in informal situations as "Mom" or "Ma." Some people, especially as adults, are on a first name basis with their parents and call them by their names.
Some call their mother's mother grandmother. Others will use the term granny or umma. Some families will use first names or gramma and a last name.
Your mother-in-law. Or, call her by her name.
You still call her your mother in law or if you were divorced you would call her your Ex- mother in law.
shivaji's mother call shivaji as shurba
You would call your mother's sister an aunt.
Your grandmother.
Your grandmother.
your great grandmother
your great grandmother
Your half-sister's mother may be your mother, if you have different fathers. If you have different mothers and your father is married to your half-sister's mother, then you probably should call her "mother." If your half-sister's mother is not connected to your father (i.e. her father married your mother) then there is no relationship name for you to call her mother, other than "my half-sister's mother."
You can call her by her first name or if your comfortable some son-in-laws call them mom.
The mother of your wife is your mother-in-law.
Your mother's mother would be your grandmother.