When talking about making or cooking food you use 做.
我昨天晚上做晚饭。Last night I made dinner.
我知道怎么做蛋糕。I know how to make a cake.
（Yes, all of them are correct.）
For your question, “make tea” and “make coffee” in Chinese: 泡茶pao4 cha2 and 冲咖啡chong1 ka1 fei1 or 泡咖啡pao4 ka1 fei1
I am going to make some coffee. In Chinese we say like this: 我想冲杯咖啡。
“I am going to make tea, does anyone want some?” In Chinese: 我想泡茶喝，谁也想来一些?