yes there are fog lights installed on the touring model... i think this is a factory option Here are the instructions for installing the fog lights; http://www.handaaccessories.com/odyssey/05odyfoglight.pdf
bad cluster
Defective or misaligned brake light switch.
No you do not need a battery, but the lights and horn will not work unless you have a battery installed, dead or not.
find the burnt out fuse and replace accordingly with the same or weaker: NEVER stronger.
Honda Element was created in 2003.
The warning lights on a Honda Accord are the same as the warning lights on most other cars.
how do i wire my brake lights on my Honda 1000
check to see if you have power going to all the signals with a tester
http://www.autotalk.com/how-to/honda-element/honda-element-03-04-keyless-remote-programming-instructions.html
Does the 2003 Honda CRV have an indicator if you leave your lights on?
http://www.commandocaralarms.com/wiring/Honda/Element/