I'm the 2nd owner of a 2006, I may have the Off-road Suspension Package?

The only thing I can notice is the 285/75/16 Bridgestone Dueler A/T RH-S tires that came with the car including an unused spare tire matching the rest.

What other things can I look for to confirm this package?

What does this mean for non-off road driver? I read about the locking rear diff, higher ratio. Does this stuff effect daily driving, for example gas mileage

 

If you have the Adventure model, then you will have a switch at the right hand end of the row that has the 4WD modes on the left end. It will have a graphic showing two front wheels turned to the right and two back wheels with an "x" on the axle between them. That means you have the off road suspension. The 285 tires could have been added without the Adventure package.

The larger tires will affect your gas mileage, how much I can't say but I would not suspect a great deal. If you never leave the pavement you might consider going to the 265's the next time you need shoes. The rest of the package probably only impacts you in a slightly stiffer ride.

 

That X button is the rear locker that comes on the offroad package. It will also have a lower transfer case. 4:1 instead of 2:1.
The shocks and larger tires are the only other specific items and usually a trailer hitch is included in those packages.
Depending on how extreme you get wheeling those added things help.
The non-adventure is still a capable wheeling vehicle and some people have used them well.

 

Yes I have the button on the right side of the of center console with the two wheels turned and an "x" on the back. Also have the trailer hitch on the back as well with the 12V socket.

Thanks for the input, now I know I have the off-road package.

 

Suggest you get out in the dirt and see what all those toys are for!

I have a Lux without the offroad package and its still fantastic at bouncing over sand dunes. If you don't take it off road you don't know what you're missing.

 

I will eventually, friend has a jeep and people from his local club go offloading. Plan to join him on his next trip.

Does anyone know if the trailer hitch is removable?

 

Look at the RPO sticker in the glove box. Z85 is the off road package. The sticker in the door will also say 285 tires over 265

 

It's removable but a pain to do just for offroading. I have only bent one of the safety chain tabs once. I usually stick a tow hook in mine when off road. The rest of the time it has a three ball hitch stuck in there and a boat following me.
It can save your bumper at times.

 

The Hitch (if OEM) does not affect wheeling, so why would you take it off?

 

Congrats! If you have a 2006 like you posted in the OP AND you have the "X" on the last button to the right you have an ADVENTURE PACKAGE equipped H3.

Some food for thought:
Adventure Package 06-10 I5 equipped H3/H3Ts
OffRoad Package 08-10 Alpha (V8) equipped H3/H3Ts

Post up some pix of your rig!