I want to eventually take photos of the lighting in stores where they might sell the model of camera I would use. How can I make it so it doesn't look like I stole the camera, just because they sell it?

First, you probably have a cell phone on you, and if it is any recent model, there may be identical ones for sale in the shop too. Yet nobody would think you stole it, just because you have it. Because it is expected that everyone have a phone nowadays

So preferrably you should not even get to the situation where you may be asked about the camera. There are some ways around it :

 - Take the pictures with the phone

 - Bring in your SD card and batteries, use the shop's camera to try it out, and take your card and batteries

 - Show the camera when entering the shop. In some "big" shops here there you can ask the security guy in the entrance to slap a label on stuff you bring in (the label reads BROUGHT IN BY CUSTOMER) to prevent confusion. However at the same time he may ask you to not take pictures in the shop. Better take pictures before anybody tried to forbid it..

Without that, you may be asked and the outcome really depends on the store owner. For most of them, if your camera have some signs of wear and tear from use, then it is not new one from the shop. If there are pictures on it that were taken outside the shop before the ones in the shop, this is another evidence that the camera is yours. If you use old camera that is not sold today then its quite a strong proof. For shop owner who thinks everyone of being guilty untill proven innocent, or if he mistakes you for somebody else who he remembers as being shop lifter, i have no idea. He will probably raise big stink before even trying to understand the situation

As for taking pictures - If you can go there you can take pictures there. I dont know what if there is a sign that forbids it, but i never seen such sign in a shop. This does not mean that you won't be confronted for it - some shop owners may not like it, some may think it is forbidden, some mey think you take pictures of their security arrangements to plan a break in..... and may start a fight over it even when it is not wrong in any way

I don't like cell phone cameras for lighting, as they are generally inferior to better DSLR/MIL (Mirrorless Interchangeable Lens) cameras.

You have two choices of poison:

1- Bring your DSLR in and get major hassle for it.

2- Use your phone's camera and deal with the "inferior" image quality.

I uses my Canon SX150 IS compact camera for long time, and makes great images and videos of lighting and even some spectra.

Maybe have a special note that the camera was brought in.