How do I find out if the wipers on my 2006 H3 Hummeris on a relay?

Your best bet , have a qualified repair shop check it out . The windshield wipers / washer are controlled by the BCM - body control module .

Wiper/Washer System Description
The body control module (BCM) controls wiper motor low speed operation. The washer pump and high speed operation are controlled directly by the wiper/washer switch. The windshield wiper/washer switch supplies voltage on the signal circuits to the BCM for windshield wiper/washer operation. When WASH, MIST, DELAY, LOW, or HIGH is detected, the BCM energizes the wiper micro relay by suppling voltage to the relay coil. This allows battery voltage from the WIPER fuse to flow through the relay switched input then through the contacts and out the relay switched output to the wiper 2 relay switch contacts. Since the wiper 2 relay switch contacts are normally closed to the low speed circuit of the windshield wiper motor, the motor will operate at low speed.
The BCM is the gateway to all the modules on the vehicle , all are connected to a serial data network for sharing info.
Having a factory or some other type of a professional scan tool that can view BCM DTC'S - diagnostic trouble code's would be the first thing in the diagnostic procedure . If the BCM or wiper switch is causing a problem - shorted etc... it wont allow the BCM to message other modules , like the anti-theft system or engine computer , so the PCM/ECM - engine computer wont see message for the request for start . You need to know how the start system works also.
Circuit Description
Moving the ignition switch to the START position signals the body control module (BCM) that engine crank has been requested. The BCM verifies that theft is not active and sends a serial data message to the powertrain control module (PCM) requesting engine start. The BCM also energizes the RUN/CRANK RELAY. When the RUN/CRANK RELAY switch side closes, and the vehicle is in Park/Neutral or with the clutch fully depressed, if equipped, supply voltage is applied to the PCM CNTRL relay coil. The PCM verifies the transmission is in Park/Neutral or if the clutch is fully depressed, if equipped. The PCM will then ground the control circuit of the PCM CNTRL relay, closing the switch suppling voltage to the starter solenoid. On some vehicles the starter will continue to crank the engine with the key released until it starts, the crank command has timed out to prevent excessive heat build up in the starter circuitry or the PCM receives an engine run flag.
There is nothing your going to be able to do , nor should you try . So do yourself a favor an take it to a qualified repair shop.

This is a complex wiper circuit ! The place to start would be to check for DTC'S - diagnostic trouble code's .
DTC B3715, B3716, B3717, B3718, or B3719
The body control module (BCM) controls and monitors the state of the ON/OFF wiper relay control circuit. When the windshield wiper switch is placed in to a low speed setting, a signal is applied to the BCM. The BCM then applies battery positive voltage to the coil side of the ON/OFF WPR relay through the relay control circuit. This energizes the relay, allowing battery positive voltage from the FRT/WPR fuse through the switched side of the ON/OFF WPR relay through the HI/LOW WPR relay and to the windshield wiper motor. Ground is applied at all times to the coil sides of the wiper relays and the windshield wiper motor from G105.
• DTC B3717, the BCM detects a low voltage level on the supply circuit of the wiper micro relay for 1 second when the relay is energized.
• DTC B3718, the BCM detects a high voltage level on the supply circuit of the wiper micro relay for 1 second when the relay is de-energized
Your best bet mite be to take your vehicle to a qualified repair shop !

Thats what you get for buying a (Over) Price toy (Guy) The control arm probally come on hooked some how. From the wiper.

Check the wiper fuse in the fuse box

Could be a bad ground wire for the low beams and or the hi/lo switch for the headlites

check the fuse, relay or it could be a loose plug into the switch, or ba switch.

there is a plastic part looks like a cap on the wiper transmission(those are the bars that move the arms) that wears out and causes the the bar that moves the passenger arm to fall off this is the second time its happened to me you have to buy the wiper trans assembly

having same problem . no burnt resister or wires but no fan

Check your fuses. Or the wipers might be on a relay.