The two pipes on your furnace are for combustion air and flue gases. Hopefully, the system is tight and it has a net neutral effect on the air in the basement. The gas water heater also needs air for combustion and the flue gases draft additional air as they flow into the flue. Usually, a basement has enough air volume to support the water heater combustion. However, other appliances, such as a dryer, can also be competing for air in the basement. Additionally, other exhaust fans within the home can also be pulling air from the basement.
I think the first place to start is with the water heater. Run the hot water heater until the burner comes on. Then, check the flue to make sure that air is flowing into it. You can do that with an incense stick or carefully with you hands (if you feel hot air coming out of the flue entrance, it is backdrafting). If the flue is backdrafting, it likely is the issue. If hot air is not coming out of the flue, run the furnace too and recheck. Then, try the dryer. Continue with various exhaust fans in the home until you find what may be causing the issue. In the end, you may need to install a makeup air duct to provide combustion air for the water heater.
If you are having issues with moisture in the basement, you should be checking your roof drainage and the grade around the foundation to make sure that excess water is not being put around the foundation. I also recommend that all basement have a dehumidifier set up to operate constantly on the humidifier control. I recommend setting the control for 60% and set the unit up to drain constantly into a floor drain rather than using the reservoir.