I met an American woman who was an English teacher. I met an American woman who was an English teacher.

If she still is an English teacher, or you met them recently, I would say, "I met an American woman who is an English teacher."

I met an American woman who asis an English teacher. I met an American woman who is an English teacher.

I met an American woman who asis working as an English teacher. I met an American woman who is working as an English teacher.

I heard that Sshe likes Anime and Manga. I heard that she likes Anime and Manga.

Or, "She told me she likes anime and manga" if you heard it from her. (The way you wrote it isn't wrong, it just sounded like this was in the past. If it's recent you can still use "I hear that she likes anime and manga," but only if you heard it from someone else. )

I hear that Sshe likes Aanime and Mmanga. I hear that she likes anime and manga.

I heard that Sshe likes Aanime and Mmanga. I heard that she likes anime and manga.

I've never known a foreigner who likesd anime. I've never known a foreigner who liked anime.

I've never known a foreigner who likes anime. I've never known a foreigner who likes anime.

I've never known a foreigner who likes anime. I've never known a foreigner who likes anime.

Anime is made for Japanese people, but she enjoyed watching animeit. Anime is made for Japanese people, but she enjoyed watching it.

Anime is made for Japanese people, but she enjoys watching anime. Anime is made for Japanese people, but she enjoys watching anime.

Anime is made for a Japanese audience, but she enjoys watching anime. Anime is made for a Japanese audience, but she enjoys watching anime.

I often watched cartoons 5 years ago. I often watched cartoons 5 years ago.

I often watched cartoons 5 years ago. I often watched cartoons 5 years ago.