Hi Ayush, welcome to the community
If you are a beginner and this is your first time building a quadcopter, then I would strongly suggest against taking the DIY route, unless you have an underlying purpose, probably a college project or something.
If that is the case, then also, do not take the DIY route on the Flight Controller unless you have have command over embedded systems and programming arduino devices, because your chances of getting success, well let's be honest, are quit slim.
That being said, and my apologies for scaring you, let's get back to business. I'll answer your questions one at a time to the best of my ability.
1) Which sensors are really necessary for my quadcopter ?
A: For the most basic version of a flight controller, you need to measure two things, what is the change in the angle of the quad in all the axes relative to normal plane, and how fast that change is occurring. Basically angular displacement and angular acceleration. You can measure displacement using a piezoelectric gyro and rate of change of the angle using an accelerometer. These days you get 6DOF or 10DOF IMU sensors which do the job quite well, some examples are :
http://f4k3url/2mdb2kIhttp://f4k3url/2nbdwET , you can find others too, pick one based on your choice
2) Can the motors be directly connected to arduino nano (flight controller) ? if no then how can i connect them (i guess using l298 modules)?
A: no, you cannot connect the coreless motors directly to arduino, it will be dead in no time. Arduino board shells out a maximum of 150mA of current on the PWM pins, and these motors (am assuming 8520 coreless ) consume somewhere between 750mA to 1.2A current. You have to use a motor driver definitely, L293d might work, but am not sure if it can handle the current draw of two motors simultaneously, I'd suggest you use high drain Mosfets and create your own H-bridge.
3) Which would be better 2.4 GHz NRF24L01 or 433 MHz wireless rf module ?
A: NRF24L01 hands down, better range, better connectivity. 433 MHz modules are piece of crap, keep them to your mini projects only.
4) How to select right motors and modules according to battery output ?
A: Its the other way round actually, you don't select the load according to the battery, you select battery according to the load. In this case, a single cell LiPo would do the job, check this out
http://f4k3url/2lOAOjG . And please, do not attempt making your own battery using mobile cells, its futile.
Creating the TxRx system is a whole different ball game pal, if you get any success in this, do ping me, i'll be more than interested.
Cheers