For you to be considered Danish tax resident when arriving in Denmark, one of the following criteria should be met:
Even if you have an accommodation available in Denmark, you will not be considered as tax resident until you have actually stayed in Denmark. Short stays in Denmark related to vacation or similar will normally not trigger tax residence, but stays related to working, will as a main rule trigger tax residence in Denmark from day one.
As a Danish tax resident, Denmark has the right to tax your worldwide income and assets. This will, however, not be the case if you are considered tax treaty resident in a country that Denmark has a double tax treaty with.
Yes, but the Danish taxation is generally limited to income and assets, which are sourced in Denmark. E.g., work performed in Denmark for a Danish employer.