Either, "I am used to having no choice" or "I used to have no choice". This is a 24-minute lecture; where exactly is this quote? Both proper options have quite different meanings.

We use the gerund form of the verb after "used to" to mean "accustomed to"--example: "He was not used to driving on the left side of the road when he moved to England." We use the simple present form of the verb after "used to" to mean something was typical in the past--example: "He used to live in China." "He used to have a dog named Lucky."

v to (be)+used to+v ing=he began in the past and still happening EX: Egyptians are used to protesting used to + v "inf" = no longer make it in present Hosni Mubarak used to govern Egypt

Looks good to me!

I'm used to doing something, meaning I like to do something or I do something very often; I used to do something, meaning I liked to do something or I did something very often in the past, but now I don't like or do it anymore. No "I used to doing" at all.