Powering up raspberry pi 3 b+ with one 11.1V 3S 2200mAH 30C Rechargeable LiPo Battery
Will LM2596 become too hot when supplying power(2.5A) to raspberry pi?


The LM2596 is just a chip; how hot it gets under a specific load condition (that is, in- and output voltages and output current) depends on the design of the circuit and the layout of the board and the cooling attached to it. So, this is up to you! Read the LM2596 datasheet, it comes with design recommendations.

If saying "module" means you're buying a ready-made power supply: Why are you asking us, not the documentation of the seller? A supply needs to come with a datasheet. No datasheet, no sale. Simple as that.


  Some suggest to use XL4015 5A because it won't be too hot when supplying power to raspberry pi since rated current for raspberry pi is 2.5A. However, I'm worry that will the raspberry pi draws too much of current since XL4015 can supply max 5A. 


You just said it draws 2.5 A. We can't tell you which requirements are correct, it depends on your modelling, and of course what you attach to the pi, and what computational load you put it under. 

So, we can't tell you whether 2.5 A or > 5 A are the necessary current sourcing ability. Only you can.

Personal assessment: 2.5 A at 5V is 7.5 W. That's a lot of power, I doubt the Pi draws more than that. 


  after I adjusted the output voltage to 5V for raspberry pi (when lipo battery is fully charged), will the output voltage from these voltage regulator drops if the input voltage from lipo battery drops (after powering raspberry pi for a period of time)?


These are voltage regulators. Their job is to regulate the output voltage, even if input voltage varies. So, no. 

Notice that the raspberry pi is not a device you want to run off batteries. It's not made with power-efficiency in mind; its SoC is from a line of SoC meant for TV set-top boxes, not for battery-powered things like smart phones. If you need something that runs off batteries for a long time, something else would be a better choice.