Questions & Answers about Из крана течёт холодная вода.
из indicates movement from inside something, so из крана means “from inside the tap.”
с usually means “off” or “from the surface” (e.g., с стола “off the table”).
от indicates origin or separation in a more abstract sense (“away from”), but sounds odd with кран. Thus из крана is the natural choice.
холодная is an adjective modifying the noun вода (“cold water”).
холодно is an adverb (“coldly”), which would describe how something happens, not the temperature of the water. To describe the noun itself, you need the adjective in the correct case.
Past imperfective (ongoing past action):
Из крана текла холодная вода.
Past perfective (it started flowing):
Из крана потекла холодная вода.
Future imperfective (will keep flowing):
Из крана будет течь холодная вода.
A common transliteration is:
Iz krana techyot kholodnaya voda
To indicate stress:
iz kra-NA te-CHYOT kho-LOD-na-ya vo-DA