沸く and 沸かす: boiling water and bringing water to the boil
Distinguish water reaching a boil from heating it to boil, and avoid equating merely warm water with boiling water.
Check whether water has boiled
お湯が沸いたら、火を止めてください。 asks someone to turn off the heat once the water boils. 沸く, read わく, describes reaching a boil; 沸いた is its ta-form.
まだ沸いていません。 means that the water has not boiled yet. It can already be warm without having reached the boiling stage.
Someone boils water
お茶を入れるために、お湯を沸かします。 means that someone will boil water to make tea. 沸かす, read わかす, uses を for what is heated to boiling.
やかんで水を沸かしました。 says that someone boiled water in a kettle. Both 水を沸かす and お湯を沸かす are possible; お湯 does not restrict the latter to reboiling water already boiled.
The result and a figurative meaning
沸かしたお湯を少し冷ましてから注ぎます。 means that the speaker will let the boiled water cool a little before pouring it. Boiling and the temperature at pouring are separate stages.
逆転のゴールに会場が沸きました。 says that the venue erupted in excitement at the goal that put the team ahead. With 会場 as the subject, 沸く can describe people's excitement figuratively rather than boiling water.
Does まだ沸いていません mean that the water must still be cold?
Show the answer and why
No. It says only that the water has not boiled yet; it may already be warm. Distinguish a temperature increase from reaching a boil.