The game consists of few completely different parts (visually, stylistically, etc). Is it possible to replay only one specific part? Or if it is not yet are there any plans on adding this in the future?

Short answer (no spoilers): Yes it is possible.

Slightly longer answer: You are able to reset the game to go back to the beginning of these individual sections after you completed the game for the first time (once you unlocked this feature you can use it at any point in the main menu).