What causes the charging and fuel light to be on at same time while driving?
The charging system light and the fuel light could be two different problems. First check the charging voltage. It should be between 13.2 to 14.2 volts.
A low charging rate can cause strange things in car electronics. Repair this first then look at the fuel light. The sending unit in the fuel tank or the gauge in the dash could also be faulty.
If you can supply us with more information, like if both lights came on at the same time or symptoms such as a dead battery, please write back and we will be glad to help.