I'm just going to offer a slightly different set of corrections (though most of it is the same as torusan's).

Is the country name "Canada" related to "kanata" in Japanese!?

It's just my guess.
I wonder if the country name "Canada" is related to the Japanese word "kanata".
Let me explain why I think so.

I was reading a book which said: 

"The name 'Canada' comes from the Huron-Iroquois word 'kanata' meaning village or settlement, and the name was used by the early explorer Jacques Cartier. The word Canada started appearing on maps in the 1550s."

When I was in NL, Canada, I visited a museum.
There was an exhibition about Inuit aboriginal people of Canada. (I'm happy to have the "," taken out so it reads as "Inuit aboriginals" as opposed to, let's say, "Métis aboriginal people" or "First Nation aboriginal people", but "Inuits, the aboriginal people of Canada" works fine too)
When I saw the exhibition, I was so surprised.
The face, body, hair style, clothes, tools--they look like Ainu, aboriginal people of Hokkaido, Japan.
Inuit or Inu, and Ainu sounds similar too.
I started wondering if they might have had the same origin a long time ago. (I don't think you need to say "a long time ago" because talking about "origins" implies things long ago, but it's not a problem if you want to include it. Just remember it is "a long time ago", <em>not</em> "in long time a go")

Because A long time ago, the northern part of Japan connected to the eastern part of Russia, and Russia connected to Alaska, and from Alaska people might have moved to Canada. (As torusan says, "migrated to Canada" is also a good phrase to use.)

"kanata/ 彼方/ かなた" means far away in Japanese.
A long, long time ago, if people started moving from Japan to "far away" Canada, it make sense to me that these could be the same people. (Or maybe closer to your original sentence: "A long, long time ago, <em>maybe</em> people started moving from Japan to "far away" Canada. It makes sense to me.")

Imagining these things interests me.

And for good reason! It's fascinating! Really great notebook entry about a really cool discovery. The first time I'd even heard about the Ainu people was when reading a Haruki Murakami novel. I'm curious to find out a little bit more! :)

The country name "Canada" may be related to "kanata" in Japanese!?

It's just my guess.
I'm wondering if the country name "Canada" related to Japanese "kanata".
Let me explain why I think so.

I was reading a book. It said,

"The name 'Canada' comes from the Huron-Iroquois word 'kanata' meaning village or settlement, and the name was used by the early explorer Jacques Cartier. The word Canada started appearing on maps in the 1550s"

When I was in NL, Canada, I visited a museum.
There's an exhibition about Inuits, the aboriginal people in Canada.
When I saw the exhibition, I'm was so surprised.
The face, body, hair style, clothes, tools- they look like Ainu, aboriginal people in Hokkaido, Japan.
Inuit or Inu, and Ainu sounds similar, too.
I started wondering if they might have same origin in long time ago.

Because a long time ago, the northern part of Japan connected to eastern part of Russia, and Russia connected to Alaska, and from Alaska people might have moved {or "migrated"} to Canada.

"kanata/ 彼方/ かなた" means far away in Japanese.
A long, long time ago, if people start moving from Japan to "far away" Canada- it makes sense to me.

Imagining these things make me feel interesting interests me.

Fascinating! I think you're on to something there! I always wondered why the Inuits looked more Asiatic than the Native Americans do, so I think you have a good theory about the different migration patterns.