Can you hear the standing waves in a particular audio room with the naked ear?

Answer 1

Yes, especially in the lower frequency spectrum. Usually, bass builds up in the corners, in the back of the room because of how the low frequency wave “breaks” in that space. (Room node)

Higher frequency nodes are herder to identify and require room correction software to properly spec out.

Answer 2

Yes and no. This is tough because you're in a room that you know very well (presumably). The easiest way to go about this is to play a song and take a walk around the room. Wherever you hear something really off/peculiar, you'll know that something weird is happening there in your room (like a node).

Also, you can try putting in your room dimensions here https://amcoustics.com/ and see the results.