Will long-time storage cause damage to my car?

Depends on where you store it. Many cars have been in storage a very long time. Most important thing is to keep it on dry ground or concrete and out of the sun and weather. Disconnect the battery cables. Maybe dump some Gumout in the gas tank before you park it.

No, if you do it right.

Not if it's properly prepared to go into storage, and kept in a dry storage location.

That depends on where you store it as well as how well you prepare the vehicle for storage.  

Parking the vehicle in a climate controlled garage and taking the time to prep the vehicle prior to storing it is far better than leaving it outside exposed to the elements and without any prior preparation at all.

Not if you prepare the vehicle for storage.

Do a search for "how to prepare a car for long term storage".

There may be a video on youtube or just a link to a site with procedures to take.

I'd say fogging the cylinders with a product that keeps the cylinder walls from pitting and keeps the piston rings from seizing are 2 of the higher concerns I'd have. Putting the vehicle up on 4 jack stands keeps the tires from flat spotting.

You'll likely have rust build up on the brake rotors.

You may haave to remove the rotors and grind the rust off of the rotors so the rust doesn't get embedded in the brake pads and cause brake noise.

Of course it will jack the wheels off the ground or take them off.

THAT DEPENDS ENTIRELY ON HOW IT IS STORED AND FOR HOW LONG. 

it will deteriorate sitting there keep it out of the weather and sun Ive seen plenty of cars sit for a few years then they are oil leakers once they return to the road other times Ive seen suspension bushes go hard and chop out pretty quick one it was back on the road.