If they are very good friends you just tend to say, "OK see ya" It's a very short way of saying goodbye and see you later all in one sentence.

If I were to be in a race and I was not last but the one before the last person, we say I came second last in a race. If you were to see a row of items and you want the one at the back before the last one you would ask for the second last one. If it was the third one from the last item you would ask for the third last item.

Don't is just an abbreviation of the words do not. They mean the same thing and are used in the same context. eg: "Do not go that way" is the same as "Don't go that way". English native speakers tend to use the word "don't" as it is quicker to say. And yes you can always write "Don't".