I think it is a mixed answer. I have always bought meds over the counter. Last week for the first time I was asked for a RX for ambien at one place. However I went to another where I have purchased it in the past and was able to get all meds I needed.
1)You can not get certain meds such as codeine type and some so called "psycho tropic" basically the triple script things from the states.
2)You have to know the generic name or compound.

as to cost,, I can get most drugs here for less ( lately, slightly less) than the cost of the co-pay on my insurance.

Basically I only get them here if I am low or for some like the ambien that require a rx in states.

Last week I went to a dentist and was given a " rx" for antibiotics Pharmacist looked at it gave me the antibiotics and handed the rx back to me. Said not necessary.

Credit cards. I am rarely asked for any ID but when asked sometimes I use a NY DL and sometimes a non official photo ID with a number no one has ever questioned them.