Thanks
If you a have labeled dataset you can use both. If you have no labels you only can use unsupervised learning.
It´s not a question of "better". It´s a question of what you want to achieve. E.g. clustering data is usually unsupervised – you want the algorithm to tell you how your data is structured. Categorizing is supervised since you need to teach your algorithm what is what in order to make predictions on unseen data.
See 1.
On a side note: These are very broad questions. I suggest you familiarize yourself with some ML foundations.
Good podcast for example here: http://ocdevel.com/podcasts/machine-learning
Very good book / notebooks by Jake VanderPlas: http://nbviewer.jupyter.org/github/jakevdp/PythonDataScienceHandbook/blob/master/notebooks/Index.ipynb