Pruning in Decision trees
Can you clarify pls, where is the suggestion, that we have to select max depth for pruning? As you said it is supposed to be done automatically due to some criterion. 
Here is some example of post-pruning: 

https://stackoverflow.com/questions/49428469/pruning-decision-trees

Yes, we should select 'K' fold to leave some data for the test of pruning efficiency. How many? It depends on your data. You can check out this Stanford lecture slides, for example, where K = 10 is suggested:

https://web.stanford.edu/class/stats202/content/lec19.pdf 

as an example. Usually, the K will depend on the size of your data, based on the size of the test fold you want to leave out.