First, and most important, your basic thought about present and past is correct.
Do you want me to turn on the fan?
is proper present tense
Did you want me to turn on the fan
is proper past tense.
Second, "open a fan" is so unidiomatic, at least in the U.S., that many would have no understanding of what you intended. (Someone repairing a fan might open it to replace a part or examine it, but that is not your intended meaning at all.)
Third, the sentences about "put" and "number" are not grammatical.
You just used the right rule in your other sentences. You start a question in the present tense with "do" (or "does"), and you start a question in the past tense with "did." So
do you want me to put
for present, and, for past.
did you want me to put
However, "put" is a transitive verb, which means it requires an object to be grammatical. So
In what number do you want me to put it
is grammatical and present tense, and
In what number did you want me to put it
is grammatical and past tense.
Unfortunately, neither is incomprehensible. I suspect that you are thinking about a fan that can be set to run at various speeds. How we would say that would
At what speed do you want me to set the fan
or
At what level do you want me to set the fan
or, a bit redundantly,
At what setting do you want me to set the fan.