Here's a table that may help: http://italian.about.com/library/fare/blfare153a.htm
As in Spanish, Italian language looks for the faster way of expressing ideas. You'll see that upon the different exercises. In my opinion, "I write on the recipe" would mean "I write on top of the recipe card", but as you may have seen there are a lot of cases that many words are taken out; for example, the articles that could make a sentence redundant.
It depends on the context. It might also be "over", in the sense that I am writing on a support (on a notebook, pc, etc) that lies on a recipe card. It's a bit difficult to talk about exact meaning with sentences this short. I think that "sul" as a synonym of "about" is only used after words that indicate a piece of written work such as "trattato", "saggio" (essay), "articolo" (article) or "libro" (book). The plain "scrivere sul" meaning "about" is rather archaic. Example: Un libro sugli animali = A book about animals Sto scrivendo un articolo sulle ricette di mia nonna = I'm writing an article about my granny's recipes But: Un libro di ricette = A recipe book
you could write on a recipe for multiple reasons, like to make corrections or change measurements. A lot of these sentences aren't meant to be taken literally, just used to help you practice. For example, you wouldn't take a tiger from the zoo...
That's correct but sometimes prepositions are used differently. For example, in Italian you don't put something on a plate, but you put something in a plate, i.e. nel piatto. Another example is you don't look in a mirror, you look at the mirror, allo speccio, and you don't talk on the phone, rather at the phone, al telefono. I saw one description that prepositions are little devils, and I'd agree but with practice you do start getting used to them, and your understanding of the language improves.