Chechens
In 1989, 73.4% spoke Russian, though this figure has declined due to the wars for a large number of reasons (including the lack of proper education, the refusal to learn the language, and the mass dispersal of the Chechen diaspora due to the war). Chechens in the diaspora often speak the language of the country they live in (English, German, Arabic, Polish, Georgian, etc.).
Chechens
The Nakh languages are a subgroup of Northeast Caucasian, and as such are related to Nakho-Dagestanian family, including the languages of the Avars, Dargins, Lezghins, Laks, etc.
However, this relationship is not a close one: the Nakho-Dagestani family is of comparable or greater time-depth than Indo-European, meaning Chechens are only as linguistically related to Avars or Dargins as the French are to the Russians or Iranians.