I'm firmly in the camp of separating the "functional" handkerchief from the decorative! Ideally both would be carried: one for display and one for offering to ladies/wiping the sweat from one's brow/acting as a tourniquet after a gun battle with enemy agents/etc.

There is a great pleasure in simply having a pocket square for a pocket square's sake and silk seems to work very well against the foil of a rough tweed jacket or barathea... although I do have some cotton ones which I like to think work well too.

Matching? For me it is more about adding visual interest: it would never "match" the tie, shirt, jacket etc. but would, at its best, add another element but one that is complimentary.

As to the fold I have two techniques... and they largely depend on how I feel at any one time and the pocket square itself rather than any rule in particular. The first is to pinch the middle betwixt thumb and forefinger, give a little shake and fold in half and then "stuff". The second is three folds one way then three folds the other and place so that the (hand stitched) edges show. I don't like the "perfect triangle" or "three points"... but that is just me.

As I say it is mainly how I feel. Some days I look in the mirror and think "Lime you need a pochette today" and other days I look in the mirror and think "leave it at home wide-boy". I think, what I am trying to say, is I like to have the option and don't worry too much about wearing, or not wearing, one.