Hi,
If I want to present a separate piece of information along with a text, can “P.S.” and “by the way” be used interchangeably (i.e., Wish you a very happy birthday. May your shadow never be less. By the way/P.S.
, I will come tomorrow.) or will only one specific of the two be used?
No. Use 'By the way' in your main text, to add a casual or not directly relevant comment.
PS is short for postscript. This is derived from the Latin scribere - to write and post - after. It's commonly used in letters. When you have finished writing your letter and have signed it, then write PS below your signature to indicate that you want to add a comment that is not part of your main letter. ie You have written this after your main text.
Best wishes, Clive