Regarding input to Arduino

Can Arduino will sustain on 12V 75Ah Battery ? Can i use that battery for Continuous 4hrs ?

They tend to survive better on slightly lower voltage especially the REAL Arduinos.

7 to 10 volts would be a better range so if you could step that 12 volts down just for the Arduino it would be a happier board.

Do that 75Ah will not harm Arduino ?

75Ah its the capacity of the battery, It means that if you discharge it at 75 amps during 1 hour you will discharge it(In theory). if you havent typed it wrong and it acutally is a battery of 75Ah, If you used 1 amp(which is a lot more thatn you can actually consume with just an arduino) it will last 75 hours working if it was at full charge at the beggining. How to calculate the duration of your battery depending on the current drained