Are the prepositions correct?
At the chemist's (or in a chemist??), at the drugstore, at the (or a??) pharmacy

Question

Answer

Usually 'the' would refer to a particular chemist, etc., but sometimes is used in instructions to mean whichever chemist is applicable  e.g.  'take this prescription to the chemist and get the medicine'  -  it could be any chemist.  It is equally correct to say  ''take this prescription to a chemist and get the medicine".

Answer

AT - is used for times.

At midnight," at noon",

Or contexts ex: " at work, "at school" especific places .

Answer

You may use both 'at' and 'in', depending on the context:
'She bought it at the chemist's'.
'I work in a chemist'.
'I'm in the drugstore' (emphasizing you are inside the store, not outside).

Here's an example from Cambridge Dictionary:

'Jane was a pharmacist in a chemist's in a small town'.

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