I'd like to know why you add a "d" to used to in this question:

"Do you know where I used to play?"

I understand that questions don't have a "d."



"used to" is a auxiliary verb. It is not the past tense of an ordinary verb.

If something used to happen, it happened regularly in the past but does not happen now. Similarly, if something used to be true, it was true in the past but is not true now.

She used to go swimming every day.
I used to be afraid of you.
I used to play in the garden.
Do you know I used to think there were monsters under my bed?



park green 757I understand that questions don't have a "d."

Only when the idiom "used to" is the main verb, which would make the auxiliary "did":

Did you use to play there?

Here the combination of 'did' and 'use' creates 'used'.

But in your example you have 'do' and 'know' as the auxiliary and main verb, so that bit about the 'd' at the end of 'used' does not apply.

Do you know where I used to play?

'd'-dropping does not apply only to questions. It may also occur with negation:

Negation: I didn't use to play there.
Initial negative adverbial (or 'only'):
Never did I use to play there.
Only with my best friends did I ever use to play there.