2007 Mazda CX-7, on a cold engine 1500 to 2000 rpm, when transmission switch goes to back drive position, a laud snap is heard. After couples of minutes of running engine and it goes from 2000 rpm to 1000 rpm everything is sound normal.
Is it normal behaving for Mazda CX-7? Does it mean I have to warm up engine for 2-3 minutes before start driving? (with my second car (Hyundai) I do not have this issue and can drive instantly.)

 

WOW!! I hope you got this problem solved by now, and so sorry it took me (or anyone) this long to find your question.

In a word, no, this does not sound so good to me. Any snap in the drive system is not good. It means that a lot of pressure is being applied somewhere and that something will have a short life-span.
In my 3, when its cold the rpms are usually around 1500-1700 when I first start her up in the morning, but fairly quickly drop down to a more reasonable level. This is not so much of a problem with a stick shift. I usually let her "warm up" for about a minute before taking off anyway though.

Since modern cars do not have carburetors as they all once did, a choke is not truly necessary. The fuel injection system can control that quite well w/o the need of a high cold start idle, so I'm guessing it has to do with emissions.
Catalytic converters need to get up to temperature quickly in order to work properly. I'm guessing that's why the high cold start idle. I am not familiar with this quirk you are describing as a sysmptom of the 7, but it may be normal?

Also, if you are the type to put the car in gear before the starter stops spinning, you may want to rethink your habits also. I have known people like this and its never easy on the vehicle.