What Is the Best Professional settings For NIKON D7200 with AF-S Nikkor 35mm 1:1.8G lens?

Put the camera in M mode for Manual control (or however Nikon indicate it), set the aperture to f1.8, have the subject close to the camera and the background far away and set the shutter speed so that the exposure indicator in the viewfinder gives the correct exposure.

But you do have a digital camera so you can see the results immediately and can adjust the shutter speed as necessary (longer if the image is too dark, shorter if too pale/overexposed)

You may wish to read the manual to see how to do the above.

Read the advice from Fhotoace about blurred background. Basically, you need a longer lens for good results, maybe 85mm f1.8. If your subject is small, maybe a book or a box of chocolates, and you place it close to the camera, and well forward of the background, you might get sufficient blur with the 35mm lens used at f1.8. (Not at f5.6, or f11, etc)

For best technical quality you must set the camera to Fine and High Quality, using the menu.

There is no such thing as "professional settings". Do you think we have some secret settings only known to professional photographers? There are no shortcuts, and nobody can simply provide you with a set of instructions. That camera and lens are capable of very fine images; the missing component is a photographer's competence. You must learn the fundamentals of photography and develop your skills.

You seem to mean shallow depth of field when you refer to "blur". This is an important topic in photography and something you will learn about as you study tutorials and practise with your camera. You can easily find a vast amount of guidance in articles and videos online. There's no point summarising a subject in isolation for you in the limited forum of Yahoo Answers when what you need is a much broader understanding of photography to place it in context.

There are no such things as professional settings.