I think in English we say, " I also used to come to this shop", but in question form the 'd' is dropped so "Did you also use to come to this shop?" is actually correct.

See: https://learnenglish.britishcouncil.org/grammar/b1-b2-grammar/used-to-infinitive-and-be-or-get-used-to-ing

We use used to + infinitive to talk about a past situation that is no longer true. It tells us that there was a repeated action or state in the past which has now changed.

She used to be a long-distance runner when she was younger.
I didn't use to sleep very well, but then I started doing yoga and it really helps.
Did you use to come here as a child?