It's pretty standard where I live in Ireland, to not be asked for references would be seen as unusual. As soon as an offer is made you would expect to be asked for the details of two people they could ask to to provide a reference.

That being said companies may ask for detailed references, but in most cases all they get back is a list of dates worked - as in your experience.

As for qualification requests, I've had those about 50% of the time and mainly with bigger more established companies or those in the finance sector. A lot of Fintech companies are be obliged by their clients to do full background checks on their employees.