How can I turn a midi keyboard to a stand-alone piano using Arduino or any other way?
You have many options here, although it is not as simple as you might think, if you want both a good sound and use an MCU.

Arduino (Uno) with speaker


Buy a MIDI shield and a MIDI cable
Write a sketch that reads MIDI note on and off commands (at least)
Connect a speaker to the Arduino
Extend the sketch to play the correct frequency based on the notes


Pros:


Reasonably easy
Very less hardware needed


Cons:


Very bad sound (like beeps, comparable to a toy 'piano' at best)
Monophonic


Arduino DUE or Raspberry PI


Get an Arduino Due at least (probably you can better move to Raspberry PI or similar device)
Sample a real piano (by key range, or velocity range), or get the samples from your DAW.
Read the MIDI on/off keys and decide which sample/velocity sample to use.
Add SRAM probably for the samples, or try to read it from a Flash (doubt it will be fast enough). For very good stereo multi-velocity samples expect a few GB.
Use a DAC to output the sound and connect it to some speaker system.
Note the above is a simplification


Pros:


Very good learning experience (if that is what you seek for)
Cheaper than a MIDI module


Cons:


Much time to invest (DACs, sampling, building your own 'synthesizer')


No MCU needed: MIDI Module


Buy a separate MIDI module where you can directly connect the MIDI cable to.


Pros:


No time to invest
Quality is as good as the MIDI module (much better than what you get on an Arduino at least).


Cons:


No 'learning' of Arduino
More expensive (MIDI module)