That's when me and my wife just got married.

This is when me and my wife had just gotten married.
If you are setting up a story, you’ll want to say “this is” and not that’s! “That’s when” implies something just happened.

Although we had made enough plan for this trip before left, we got some problems then.

Although we had planned enough for this trip before we left, we had some problems.

While we were on a bus, we didn't know how to get to destination.

While we were on a bus, we didn’t know how to get to the destination. You could also say, “while we were on the bus.” “A bus” implies a more general feeling.

But it seemed like there were no people who could speak English.

But it seemed like there wasn’t anyone who could speak English.
You could say no people, but wasn’t anyone sounds more natural!

Then we yelled that If anybody could speak English.

Then we asked if anybody could speak English. “Yelled” is a bit aggressive!

After we went back home, we still got in touch each other.

After we went back home, we stayed in touch with each other. Or you could say “we got in touch with each other.”