Creating a Printing Profile
Yes, you can do this. You'll use a feature called "Presets" which appears in the Print window. You can create a Preset so your color HP laserjet printer will print, by default, in greyscale (aka black and white) on both sides of the paper (duplex).

Here's some guidance.

Open a document you want to print. Go to the File menu, select Print.

The print window appears. Locate the "Preset" section. You'll see it's set to Standard. 

You're going to create a new Preset by doing the following. 

In the "Copies" section you'll most likely see a box named "Two-Sided". Check this box.

Next, click on the pop-up menu near the middle of the Print Window. The menu should be set to the name of the application you're using, such as Word or Safari. Click on this menu and select the section which lets you switch from color to greyscale. (For my Brother color printer the section is named "Print Settings" but HP may use a different section name). Select the greyscale option.

Now that you've selected 2-sided and greyscale, then click on the Presets menu and select "Save As". Give your new preset a name. I suggest "2-sided greyscale".

Print your document by clicking the Print button.

You've now created a Preset which'll be available in all applications so you can easily print duplex, greyscale documents. This Preset will be the default until you select another Preset to use instead.