What documents will I need to show at a CBP internal checkpoint?

You should bring your I-485 receipt notice (I-797 notice) and if you received one, an employment authorization document (EAD).

I assume that you are currently in the United States and entered before you filed your I-485. When you filed your I-485 application, you should have concurrently filed forms I-131, for a travel document, and I-765, for a work authorization card. The travel document along with your national passport should be all you need. The travel document allows you to travel in and out of the United States while your I-485 is pending.

Since you are adjusting your status to become a lawful permanent resident, you should take with you the following: your passport, the approval notice of the I-526, the receipt notice of the adjustment of status application, and the employment authorization card if already issued.

Your I-485 receipt should serve as sufficient evidence that you are authorized to remain in the United States while your application is pending.

The I-485 receipt does not show valid status - present the EAD card.

You could travel with the I-526 approval notice and I-485 receipt notice if you have not received your EAD/travel permit combo card after filing the I-485 packet. If you have that EAD/travel card, that will be all you need to travel and work anywhere in the United States.

If you have a receipt for the filing of the I-485 it might help, but I am not sure that will be enough. You should check with CBP before you set out.

Internal checkpoints are very limited and rare, unless you are very near the border. Nonetheless, have your current passport, the expired I-94, as well as the I-485 receipt notice.

You need a valid visa or a green card to enter the United States. We would need to know much more about your case to answer this question.