PRINCE2 uses a predictive approach, while agile methodology uses an adaptive approach.
No, you don’t need PRINCE2 for agile.
No, they are not the same as they carry out different functionalities.
Yes, you can combine the two. You can use some agile methods together with PRINCE2.
PMP is better than PRINCE2 since PRINCE2 focuses more on frameworks and processes while PMP focuses on all the techniques and frameworks of project management.