DIY subwoofer kappa perf 12, can I use real wood ?

You'll get more responses from people here who are more "subwoofer guru" than I am, but I'll try and respond to some of your questions:

Is it a good idea to use this car subwoofer to make my home theather/music sub ?

In general, no it's not a real good idea, but it can work. It really all depends upon the specs of the woofer. As long as you can acheive the response you're after, it can work. In general, woofers designed for auto sound have slightly different parameters that often make them less than ideal for music or home theater installations. Better woofers designed for music or HT use may have lower distortion motors (shorting rings, etc.) but lower sensitivity, for example.

Can I use real 1 inch thick solid maple or birch wood to make the box or its better to use the MDF boards and wood laminate or carpet ?

I wouldn't recommend building the box from maple or birch. Although I hate MDF (nasty stuff, really), its properties are just about ideal for speaker and subwoofer boxes. It's heavy, dense, and essentially non-resonant. Also-- and this is important-- it's more dimensionally stable than real wood, and it will be much easier to build an air-tight enclosure with MDF. Less expensive, too. You can finish it however you choose.

The BASH amps are fine.

The stuffing amount/material will be highly dependent upon the actual enclosure that you end up building. A sealed box generally can be stuffed, while a ported enclosure might not need as much.

Box? I picked this one up from partsexpress. Well built and finished.

http://www.partsexpress.com/pe/showdetl.cfm?&Partnumber=302-820

well the specs look good on that speaker!
How does it sound?
What is good about DIY is you can build the sub to the size that fits best in your application.