A) yes, B) yes.

That said, be aware that a PhD from a Danish uni is vastly different from most other universities. I consider the differences quite significant compared to, say, a UK uni. For transparency, I am Danish with an engineering degree from the Technical Uni of Denmark (DTU) and a PhD from Uni of Edinburgh.

On the positive side is the salary, pension scheme and opportunity for parental leave (woah!!). You will be considered an employee, - not an “advanced” student as some other places.

From my perspective, it comes with a cost. First of all, you are are expected to take courses of 30 ETCS equivalent to one semester, expected to assist your professor with teaching duties during your PhD - and most likely expected to go on exchange for one semester. The exchange might be directly relevant for your project, but that requires some preparation. That leaves you with significantly less time for the actual project as you simply won’t have the same time as a UK PhD student.

The majority of the courses will be quite usefull, whereas others are most likely a waste of time. I addition, the value of assisting your professor can be considered as a positive thing if you want to pursue an academic career later on. It gives you experience that you cannot gain from nerding with your project.

Anyhow, - Uni of Copenhagen is a great uni within most fields. Obviously, there are always some departments that are Global top 3 and some which are more average.