I am really new to this, I am planning to build my own tricopter drone which can be controlled via raspberry pi using wifi and use Arduino as a flight controller to communicate via USB. I am hesitating on which battery to pick as I am planning to keep drone for longer time (more hours for recording) at least 4 hours. So I am thinking to use a 45C 11.1V 4500mAh battery with 30A esc and a C2204 1200kv motors which draws 11A, the battery will feed power for all 3x30A esc and 3xMotors question is will it damage the esc? if it will damage the esc which esc do I need? and will the battery power motors, raspberry pi and arduino all together?
A larger battery can supply more current, but will only supply as much as the motor and ESC pull from it. Once the battery is large enough to provide the power the motor needs, making it larger won't increase the power - much like increasing the size the fuel tank in a car won't change the engine power.
If your motors will only draw 11amps, you don't really need 30amp ESCs. 20amp ESCs would be fine, unless there's a chance that you might want to switch to 4s (14.8v) batteries and push the motors harder in the future.
will the battery power motors, raspberry pi and Arduino all together?
I think the pi and Arduino require 5v, and they would probably like to be isolated from the electrical noise of the motors and ESCs. The usual solution for this is a PDB (Power Distribution Board) with a 5v output. This is a simple circuit board that splits the battery power to multiple solder pads to simplify connecting up the motors. They often also contain filtered 5v and 12v outputs. They're only about $5 so most people use them.
The alternative is to use fixed-wing ESCs, which usually have a 5v supply built in. This is called a BEC (Battery Eliminator Circuit, from the days when people carried a separate 5v radio battery) and supplies 5v on the red wire of the receiver plug. I wouldn't recommend this though, as multicopter ESCs will generally have a faster and smoother response, and support a range of high-speed protocols such as DSHOT. Also it's generally considered a bad idea to connect more than one 5v supply, so you'd be paying for and carrying 2 unused BECs.
I should add that a 4500mAh battery is a lot for three 2204 motors to lift. Half that size would be considered a large battery. I would suggest starting with batteries that are half or even a third of that size. That way you can have a light machine for testing and then parallel two (or three) batteries together to see how it flies with the extra weight. Two smaller batteries will probably cost about the same as one larger battery.
There are a few numbers on the motor, battery and ESC which you should compare to check they are suitable.
Your motors have a current requirement (here, 11A) and your ESC must have a higher current rating than this; your 30A is very overrated but would work.
The ESC should state its acceptable voltage range - this is usually given as a voltage (e.g. 11-17V) but may also be given as the number of battery cells in series (e.g. 3S-4S.) You must use a battery which matches this range.
The battery will state its safe discharge rate (in C) and charge available (mAh.) The maximum discharge current is the 'C' rating multiplied by the battery charge in Ah, so a 45C 4500mAh (or 4.5Ah) battery can deliver a peak of $45 \times 4.5 = 202.5A$.
For your example, you've not indicated the ESC you plan to use but as most are 3S or 4S you are likely to be OK there. The discharge rate on a 4500mAh battery would be $(3 \times 30) \div 4.5 = 20C$ continuous at full ESC current (or closer to 10C with those motors.)
By using some form of Battery Eliminator Circuit (BEC) or voltage regulator you should be able to use the battery to power the Raspberry Pi and Arduino.