There is very little crime in Switzerland, Graubünden being one of the safest cantons. There may be areas of Chur that could be dodgy after dark.
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In most of the canton, German is the official language, but the main language in these areas is Alemannic, or Swiss German as it's called. The northern part of the canton including Chur speaks High Alemannic dialects and the southern parts Highest Alemannic dialects. In some parts the official languages are Italian or Romansh, with many parts bilingual in German and Romansh.
You should be able to manage with English, especially, but most certainly not only, in the German-speaking part, but the most convenient lingua franca is German; since both "German"-, and Romansh-speakers are usually taught German in schools, it is a language you can speak with the vast majority of the people in the German-Romansh bilingual parts. Even in the unilingually Italian/Romansh-speaking parts, people will often speak the language since even there they are taught it in school.