Can the Battle Master fighter's Know Your Enemy feature "see through" the Disguise Self spell, shapeshifting, or similar abilities?

Question

The Battle Master fighter has the 7th-level feature Know Your Enemy (PHB, p. 73):

Starting at 7th level, if you spend at least 1 minute observing or interacting with another creature outside combat, you can learn certain information about its capabilities compared to your own. The DM tells you if the creature is your equal, superior, or inferior in regard to two of the following characteristics of your choice:

• Strength score
• Dexterity score
• Constitution score
• Armor Class
• Current hit points
• Total class levels, if any
• Fighter class levels, if any

Say a creature is under the influence of a spell or ability that changes its appearance or shape, such as the Disguise Self or Polymorph spells or even a dragon's Change Shape action.

Would the Know Your Enemy feature reveal the true stats of the creature or something else?

Answer 1

You observe the current statistics of the creature

Disguise self is an illusion that only changes your visible looks. Your actual game characteristics do not change. There are not even other characteristics that you could be fooled about.

The Battle Master fighter's Know your Enemy feature (PHB, p. 73) does not state you need to see the true form of the creature, just that you must "spend at least 1 minute observing or interacting with another creature outside combat", which you can, and you will be able to learn about its characteristics.

The description of the Polymorph spell, however, says (emphasis mine):

The target's game statistics, including mental ability scores, are replaced by the statistics of the chosen beast.

As both the terms statistics and characteristics refer to things like ability scores, hit points, AC, we can conclude they mean the same and can be used interchangeably.

The new statistics replace the original creature's statistics. What your character can observe are the characteristics of this creature, not of the original creature.

Know Your Enemy learns about the characteristics of the observed creature.

You can use this as a test in general: Are the game statistics of the creature actually replaced or modified (rather than just their appearance being changed)? Then these are the statistics you learn about.