Yes, that really is confusing and difficult. And no, you do not have to use these fillers/modal particles. However, since they are often used to make a statement or a request (as in your example) sound less like an order, you may want to be extra careful to always use the polite form (conditional). E.g., in the example you quote, you could just use a question, e.g. "Würdest/Könntest Du (bitte) den Salat waschen?" And I'm sure that eventually you will have heard these particles so often, in so many different sentences, that you will just know how to use them :) Does that help?

You don't have to use these "flavor words" as a beginner. I consider them an advanced feature of the language to build some subtle nuances into your sentences and make them sound more natural. But the sentences also work without them. I am currently struggling with similar concepts in another language. My strategy is: Learn to recognize them and try to find out, which additional meaning they put into a sentence. But I don't use them actively as long as I don't feel comfortable in where to put them. So this might still take quite a long time.