Answer to Question 1
Patterns allow us to reuse past experience to mold present solutions. For example, in taking an exam, we use our previous experience of timing ourselves and reading questions carefully before answering the questions, although the questions and answers are never the same.
Answer to Question 2
Methodologies paint the development process in broad brushstrokes and stay clear of specific problems (though specific problems might be used as examples). Developing a software application requires a methodology. Recipes or cookbooks, on the other hand, are about very specific problems: we might make small adjustments, but the recipe assumes that its instructions, in detail, are fairly correct. Withdrawing cash from an ATM requires step-by-step instructions (or a recipe) that is always the same. Patterns describe a problem that occurs over and over again in our environment, and then describes the core of the solution to that problem in such a way that you can use this solution a million times over, without ever doing it the same way twice.
Phobos in color by Mars Reconnaissance Orbiter - HiRISE
True-color image of layers of haze in Titan's atmosphere.
Population: Historic Patterns
How to solve word problems with two unknowns (Question 4)
economic question
Conservation of organization and patterns of expression in Hox genes