Cluj-Napoca is in general a safe city. Even after dark, it is safe to walk through the city center and some of the other neighbourhoods. To be on the safe side, unless you know exactly where you're going and how to get there, suburbs should be avoided at night, especially the neighbourhoods of Manastur, Marasti, and Iris, and the train and inter-city bus station areas.
You should, as always, take care of your belongings and pockets. In the unfortunate event that your wallet is stolen or lost, it is likely that it will resurface after a while, but without the money and credit cards so be sure to call your credit card company and lock the credit card as soon as you notice it's missing.
talk
The official language is Romanian, a Romance language. Most educated people born after about 1970 will speak reasonably good English and will likely be proficient in one or more second Romance languages; most educated people born before about 1970 will speak reasonably good French and Italian. Hungarian is a commonplace language, spoken by the relatively large Hungarian minority. The Roma people Gypsies speak their native Romany, as well as Romanian, and sometimes English as well. Beyond that, as in any major city, there will be a smattering of other languages.
emergency numbers
As throughout the rest of the European Union, the police, ambulance, and fire department are reachable at the number 112.