Robin2:
That 12v 9Ah battery should be capable of powering everything. Lead acid batteries can usually supply high currents for short periods. But I can't say how long it will be until the battery needs recharging. I would assume 9Ah really means 3 or 4.You can certainly connect the battery to the Arduino. However do NOT draw current for the other device through the Arduino.
...R
PS ... do not leave a lead-acid battery in a discharged state - it will greatly shorten its life.
so how can i control the servo motor and the HC-SR04 if i will not draw any current from other devices from arduino?