My 2005 Civic engine stopped running at a gas stop.
After pumping gas, the engine sputtered and stoped.
The red icon that looks like a battery lit.
The red icon that looks like an oil lamp with oil dripping was also lit.
I started it again and drove off again with no problems afterward -- A/C running and everything.
What should I look at first or is it really not a problem?

 

The first problem was you were filling the tank at a gas station with the engine running, that is so against the law up here, [and down there] that gas stations here will turn off the pump remotely.
It also means the cars evap. system is not working, gas cap off, probably what shut down the engine. 94

 

lol i have never seen that happen before...i wonder if someone done it before...

 

Yup. It happened again.
It was at the gas stop.
Cap screwed off. Pump going. In a few minutes, engine dies.
Pump out. Gas cap on. Start engine. No problem.