So, I figured out who Shima really is and why things went down the road they did. Please take a look at the following quote:

I finally remembered. I’m not Shima Katsuki. That was the name of the person dearest to me. We spent much time together, and he left me with his last wish.
Shima Katsuki; Episode 06 12:17

So the Shima we see is only naming himself after the one dearest to him. So who is that real Shima?

Master. Master. My current master is not the same as you, but she’s a very kind person. But she makes me worry at times. Was I able to achieve the goal? Was I able to achieve the promise we made? Now, it’s been too long ago, and I can’t remember. But right now, I want to remain like this. Please allow me to be with her forever.
Shima Katsuki; Episode 06 21:17

So the master of the cat was the real Shima Katsuki. And about this promise the two made? We have to backtrack to the previous episode to answer that:

Listen well. This charm has a light in it .It’s a light that grants any one wish. You will take this and go to her. And you will grant her wish. Do you understand?
Master Shima; Episode 05 11:16

This is the quote that Master Shima told the cat. But how did this unknown person know Misae, and why did he want to grant her and only her wish?

It was back when I was in elementary school. I think you were going to the hospital to visit your mother. When you went, you cheered my up when you found me in the hospital’s courtyard. You don’t remember this? I was in a wheelchair with a cat on my lap.

I remember now. But I didn’t do anything. We only spoke for a bit.

That’s not true. You really cheered me up.

What exactly did I say?

Um… I forgot. But I really am grateful to you. That’s why I want to return the favour.
Shima and Misae; Episode 05 13:43

After acquiring a temporary human form, the cat got close enough to Misae to hear her wish, but the charm was empty. Since he couldn’t remain human forever, he continues now as a cat to fulfill his promise with the real Shima to grant Misae’s wish. And afterwards, Misae was forcing herself to disbelieve that the cat was the boy she loves, until Tomoya told her otherwise. Now that she knows and accepts this she can finally move forward to find happiness down another path.

"It's just that someone said a similar thing to me in the past."

1. voice acting
No, the cat doesn’t actually speak like Shamisen does. But at the scene at 11:17 where the Okazaki hears voices when looking at Nanashi, I assume that’s the cat’s thinking voice. Although there are some heavy post-processing effects on this sample, the pattens are very similar to Shima’s voice in the sequence directly after.

2. physical appearance
Nanashi: yellow-green eyes, light brown fur.
Shima: yellow-green eyes, light brown hair.

3. camera presence
Nanashi is making his way into a more scenes than otherwise necessary, for example when Misae is remembering the one who told her she yells because she worries.

As for the wish, if the above were true, it would probably be something the lines of “I wish I could always have you around despite the fact you have a chronic illness.”¹ (Otherwise why bother transforming into a cat and just stay human?) What I wonder now is why Misae became so attached to Shima, and also the significance of Tomoya both at when he heard those lines about the light and the charm (at 11:17) and a little earlier when Misae said she had to take care of them younglings. For an instance I thought this was related to Tomoya and his father (hair colour, avoiding some certain history, and having to visit her mother in the hospital) but I think it is too unlikely that she is Tomoya’s elder sister. Could those lights Nanashi mentioned possibly be the ones from the Afterworld? There is a resemblance in voice between the Junk Robot and Nanashi as well.

That’s all I can make out of this episode. I don’t really see how this fits into the big picture, but I guess the same could be said about the first episode of the Mei/Youhei arc. I can feel myself growing a little tired of the side characters though; hopefully we’ll get back to the main characters soon afterwards. I also don’t really like the supernatural elements in Clannad, since otherwise it is a completely down-to-earth story about the lives of a handful of high school students.