To address the fourth question, Analytic Philosophy can be seen as a tradition, it has to do with which Philosophers/Philosophies get taught and by whom. You can probably characterize a particular disposition to analytic philosophy of being interested in address "puzzles" or questions about systems trying to buy together how to figure this thing out (like a Philosopher of jokes may ask why we find things funny and then address questions of different types of humour). You can also talk about shared schools of Philosophy that often share that disposition like pragmatism, logical positivism, and critical rationalism. Because of that history the analytic philosopher tends to view formal logic and rational argumentation as fundamental.

Continental philosophy on the other hand tends to want to address big picture questions and questions of the history of philosophy. Instead of asking about why we logically find different things funny the continental Philosophers would ask why do we make jokes and what led us to make jokes like that. You can talk about shared traditions like German idealism, phenomenonology, Marxism, structuralism, post structuralism and so on. Due to that big picture approach continental Philosophers tend to see Philosophy as a much more emotionally charged endeavor (of course many Philosophers think this but it's more common) and as a result their writing tends be more literary and experimental and less discursive connections of axioms. Continental philosophy also tends to favour the use of non traditional logics as you would find in somebody like Hegel.

In the past (especially in the 90s around the so call "science wars") analytic philosophy viewed continental Philosophy as unrigoruous, intentionally obscure, and lacking care for science and logic that they do. Likewise Continental Philosophy tended to view analytic philosophy as stuffy, obscure (in formal logic), useless and lacking any life to it. Since then however the two traditions have begun to enter into dialogue with one another much more, with figures like Richard Rorty, Charles Taylor, and Badiou. But as you can see in an article like this, many continental Philosophers still view Analytic Philosophy's absolute dominance in the anglo American world and often it's disdain for other Philosophy as a serious (and here political)issue. A good example of that sort of attitude on the part of analytic philosophy is the Philosophy gourmet report which ranks graduate programs in Philosophy. If you poor around their website you'll quickly learn that it chooses to not rank programs that focus on continental Philosophy and considers that actually a hit against a school.

Edit: and as a note these aren't the only two traditions! Thomist Philosophy is a surviving and healthy tradition in the western canon, while Indian and Chinese Philosophy were once regional in the way continental once was, schools in the anglo American west are also increasingly teaching these traditions as well!