Can you elaborate please? I didn't know that there are still such conservative fractions within Lubavitch, as in focusing that much in maintaining Yiddish and it's grammar, also in regards of learning no English at all. Is this the mainstream Talmid Torah in CH you're talking about? (I actually don't know Lubavitch too well)
In Lubavitch לימוד על טהרת הקודש is an important value. Some consider Yiddish important. It's somewhat of a dichotomy, on the one hand being the language of רבותינו נשיאינו and specifically of the Rebbe, while on the other hand it's definitely not the primary language of most, and the Rebbe clearly holds that Jewish studies should be taught in a language the kids understand.
If you want to read about the שיטה you can see
http://www.chinuchtime.com/articles/Taharas-Hakodesh.zip you might also browse around his website for more.
Oholei Torah is the largest boys school in Crown Heights, and is considered mainstream.
ULY is the second mainstream school. I believe they have abandoned Yiddish a few years ago (as in no longer doing Chumash with טייטש, but rather learning and translating in English), but I also believe English curriculum is optional there.
Ohr Menachem and more recently Ohel Yosef Yitzchok are more "fringe" and extreme in טהרת הקודש and emphasis on Yiddish. I believe Cheder at the Ohel is also על טהרת הקודש, I'm not sure how much Yiddish is emphasized there.
On the other end of the spectrum is Lamplighters which IINM try to be a Montessori type Jewish School. It's definitely not mainstream, though I've heard of some "mainstream" families that might send kids who don't fit well into mainstream schools there.