This may be what you need:

http://www.adafruit.com/products/987
http://learn.adafruit.com/stereo-3-7w-class-d-audio-amplifier

I Googled "7 segment Arduino tutorial" and got this example.
It probably is close to what you want.

https://www.youtube.com/watch?v=WfdeGb0LUUY
http://www.hacktronics.com/Tutorials/arduino-and-7-segment-led.html

https://www.youtube.com/watch?v=CRJUdf5TTQQ&list=ECA567CE235D39FA84&index=10
Discusses Hardware debouncing.

Draw us a diagram of the  way you think the project would be wired up.
This will give us an idea of what you are trying to do and we can then supply some help.

WEB site mentioned here causes:

Norton blocked an attack by
Web Attack: Blackhole TooIkit
Website 20.

how much power something is really using.

You probably mean how much current.
Measure the total current the project is drawing with an ammeter/digital multimeter DMM

http://www.allaboutcircuits.com/vol_6/chpt_2/4.html

The X-10 TW523 Two-Way Power Line Interface is an option.
http://www.angelfire.com/tv2/fvazquez/docs/Electr/X-10_TW523.pdf
You could write your own protocol.

Add a resistor (about 10K) from pin 7 to Arduino +5 volts.

edit: as AWOL said

best way to power

They are equally the best, but it is up to you to set your design criteria.

The USB connection bypasses the regulator so no heat is generated on the PCB.

7.5 volts is good since there is no voltage drop or noise experienced from the USB cable. Also the Arduino regulator will give thermal/current limiting protection.

You could quickly find out by using a razor knife.
Cut a power trace, insert the ammeter across the cut, then solder the trace.

See attached images

Would you advise me to use it ?

Do you need to use a servo motor or will a DC gear motor do?

This car/kart will have to be able to climb ramps with a considerable inclination

You have to come up with some numbers and design criteria:
Speed
Weight
Incline
Forward/Reverse/Steering
Amperage/Voltage you will be using
Remote control
etc.

power my arduino from the car battery?

Yes

Will it be too many amps?

Place a 1/2 amp fuse between the battery and the Arduino.

Will my arduino use the whole amp from the battery

No

My arduino will be controlling 3 TIP120 transistors.. 1 for each color. The amps o the LED bars ten selfs will be under 1Amp for sure..

Use a 1 amp fuse for these.

It is probably surplus.
Supply and demand.

For example there are lots of these available:
http://www.princessauto.com/pal/product/8366429/Miscellaneous-Surplus/Window-Crank-Motor
OR
http://www.surplustraders.net/category/DC%20GEARHEAD%20MOTORS-0184

What you are planing is reasonable.
My guess would be a, 1000uf capacitor @ 10V or more, on 3.3v would be more than sufficient.