Can my car sit for ten without damage to the tires?

Yes you should be fine. It takes considerably longer for flat spots to form. If a tire is in decent shape, it could be months before anything starts to show up.

Most modern tires won't develop flat spots setting for extended times, at least none that won't smooth out as soon as the tire starts moving.

What you need to be more concerned about is the battery, modern cars have a lot of items that the battery keeps the memory alive in while setting, for most usage this isn't a problem because the battery will be recharged as soon as the engine starts. Now a good new battery doesn't have much of a problem going 2 to three weeks setting but if this car has an older battery it could be a cause for concern. If you have an outlet near where it will set for this long then an easy solution to this is a device called a battery maintainer. They are a very small smart charger that will monitor the battery and keep it at full charge but not damage it by constantly charging. To use them you just park close enough that you can reach a power outlet or use an extension cord and connect the clamps to the battery following the included instructions. Then plug it in. It will do the rest. Just do not attempt to start the engine with it connected, while it may not cause an issue I've heard of them failing due to the high currents drawn by the starter if there is a poor connection in the system. I use the Deltran battery tender products all the time and really like them but there are other brands out there.

Another option that would work if you are away from power but parked out in the open in an area where the sun will hit the car would be a solar battery maintainer, most of these just plug into the power outlets on a car and you set them on the dash so they receive full sun as much as possible. They also work but not if anything covers the panel, so if you're in an area hat gets snow or other things that can block the sun they are not so good.

The other option would be to simply pull the memory fuse up in the drivers side fuse box at the end of the dash. This is the method most cars are shipped with and when parked on a dealer lot are set up in. It shuts off the interior lighting and many memory items. However depending on the options your car has pulling the fuse will require some items to be reset when you plug the fuse back in. For your car these items are the Sunroof, Trip computer, Automatic climate control system, Clock, Audio system, and the Auto windows. The fuse location is shown below and is in the maintenance section of the owners manual. The reset procedures are in the owners manual in chapter 4 and are also included in this post.

For the sunroof - Whenever the vehicle battery is disconnected or discharged, or related fuse is blown, you must reset your sunroof system as follows
1. Turn the ignition switch to the ON position and close the sunroof completely.
2. Release the control button.
3. Press and hold the close button until the sunroof tilts and slightly moves up and down. Then, release the button.
4. Press and hold the close button until the sunroof is operated as follows
TILT DOWN - SLIDE OPEN - SLIDE CLOSE
Then, release the control button. When this is complete, the sunroof system is reset.

For the trip computer - All items will reset to zero with the fuses unplugged, to reset you turn the key on, press and hold the trip button until they flash and display zero, then verify that the average speed, mpg and miles to empty show zero. Once you have driven a while refill the fuel tank with more than 2 gallons to ensure the miles to gallon works properly.

If you have the automatic climate controls - If the battery has been discharged or disconnected, the temperature mode display will reset to Fahrenheit.
You can switch the temperature mode between Fahrenheit to Centigrade as follows
While depressing the AUTO button, depress the OFF button for 3 seconds or more. The display will change from Fahrenheit to Centigrade, or from Centigrade to Fahrenheit.

The Clock will reset to a default number. To adjust it to current time -
Place the ignition switch in the ON position, the clock buttons are used to set the time
Pressing the “H” button with your finger or similar object will advance the time displayed by one hour.
Pressing the “M” button with your finger or similar object will advance the time displayed by one minute.

The audio system will reset as well and to deal with this depends on which unit you have installed. However all will forget programmed stations and if you have something like an Ipod or other device that you set-up in the audio system it will need to be re-setup once the power is restored. They don't say if there are any theft codes for the audio systems but those would be on a sticker in the glove box or owners manual normally if required.

For the optional auto power windows the reset is simple -
1. Turn the ignition switch to the ON position.
2. Close driver’s window and continue pulling up on driver’s power window switch for at least 1 second after the window is completely closed.

Regarding the battery, my suggestion is a little more simplistic. If the battery is in decent shape, it should start after 10 days. If it starts, let it run for at least 10 minutes. That ought to get it charged pretty good. If it doesn't start, get a friend with jumper cables to help jump start your car. Then let it idle for at least 20 minutes. It should be good after that.

That would work, but it might also mean resetting some of the above items, so both methods have valor. I just don't like jumping any vehicle these days as it's easy to cause problems, either with an alternator that is now trying to charge a low battery rapidly or worse, if someone make a mistake during the jump starting process.

If the battery is under a year old and fully charged when you park it, it should be okay. However if it's the original 11 year old battery it becomes a questionable item. I try to err on the side of caution and prevent issues so a maintainer just takes the guesswork out and makes it one less item to think about.

It should be fine as long as it's fully charged then. Just take it out and drive it some, park it and it should be okay. You have the above information just in case you ever need it.