Answer 1 : The software package that you have for the PLC propably has a simulator that you can either find on the Internet if you lucky or from the supplier.
Answer 2 : There are no such thing as a method of programming, companies do generate standards to assist the maintenance crews on a break down, PLC language is logical, there are alot of different ways to write code that does the same thing.
They use standard function blocks that perform certain tasks for certain equipment
Whats important is to write your code in an understandable and structured way. As you become more experienced you will find good and not so good ways of doing things.
Good luck
PS the Karnaugh method is used for logical eqautions in digital systems using gate inputs, it will assist you using gate logic but i have never touched one in my 4 years in PLC's
