Although I can understand what you are trying to say, none of your sentences really sound like natural English. They are grammatical, but the word choice sounds like a direct translation from another language, and not how a native speaker might phrase the question.
As an expression of the passing of time, asking "How many years have passed since you were born" is grammatical, but odd without any context. Most people would just ask:
Do you know how old you are?
It's fine with other significant events. Some examples:
Do you know how many years have passed since you graduated high school?
Do you know how many years have passed since you last visited your home town?
Do you know how many years have passed since you spoke to your childhood friend?
"Passed on" is not a substitute for "passed since". "Passed on" or just "passed" is actually a common euphemism for "died".
Many years have passed since my grandmother passed on, but sometimes I speak to her as if she could still hear me.
"Pass on" can also describe an object (of some importance) that is passed from one person to another, usually in some formal context such as a legacy:
Before my wedding, my mother passed on her wedding ring to me, and now I'm passing it on to you, my daughter.
Keep in mind that the usage of pass in "pass since" is somewhat figurative, as it metaphorically indicates the movement of time going by. In the same way a person can "pass by" a friend without recognizing them, you can say something like:
As I get older, sometimes it seems as if years can pass by without me even noticing.
Other phrasal verbs such as "pass from" and "pass to" are possible, but more difficult to fit into the metaphor related to the passage of time.