How can I travel while on H-1B with an approved I-526 petition?

You may get additional questions at the border, but H-1B visas allow for dual intent anyway. Once you file for adjustment, you may have to wait until you receive advance parole.

I would submit the I-485 application, receive a receipt from USCIS, and then apply for advance parole to allow you to travel outside the United States while your application is adjudicated.

H-1B is dual intent no problem. File your adjustment and then go and get an H-1B, or if you do not want to go to the consulate, wait 90 days for your EAD and advance parole travel permit.

Yes, the H-1B is a dual intent visa so you may travel on that until you get advance parole with your I-485 application.

H-1B is a dual intent visa, which means you are allowed to have an immigrant intent and having an I-526 approved does not keep you bound. Thus, if you have the H-1B visa page that is good until 2018, then it is enough to travel freely. If your visa page has expired, but you have an approval of H-1B extension, you could either obtain a new visa or travel with the original approval notice. You should file the I-485 at any time while maintaining your H-1B status. Your immigration attorney should be able to guide you through this.

An H-1B visa is a dual intent visa, which means that you can have both temporary and permanent intent when you enter the United States with this visa. In order to get the H-1B visa stamp, the underlying conditions that supported the approval (working at the job) should be in place and then you can enter the country with the visa without problem.