To use an AirPrint printer the iPhone/iPad/iPod needs to be connected to the same local network that the printer is connected to. The printer can be connected via wifi or an Ethernet connection that connects to your wifi network.
If the iOS device is connected via the phone mobile data network then it can't print to using AirPrint.
Why is your iPhone not connected to the wifi network? Is it because you are trying to print to the printer when away from home? Or is it because you have a large property and you are out of range of your wifi network?
While you can't use the native AirPrint when not connected to your home wifi, you can use HP's ePrint service. This works by your printer having its own email address. You can email documents to the printer that it then prints.
The service is somewhat limited when compared to AirPrint, as you need to be able to get whatever you are printing into a document and be able to email it. So many apps that support AirPrint can't be printed from using ePrint.
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.
Best Answer
Look in /var/log/system.log and see if you can get more information about the messages. Also look at the settings in /etc/syslog.conf