等待 and 等候 , these two verbs are pretty close, sometimes even interchangeble. The first one is used with a particular object 等候消息，等候命令. Compared to 等候，等待 has more "emotional weight", it contains "期待"的意思 "anticipate"，"await with pleasure". 等一下/ 稍等一会/等一会儿 you can say it to someone, it means "wait a second", "just a minute"

Hey Sandra, 都等 isn't a word, rather two separate words 都 meaning all and 等 meaning wait. 等一下 is again two words. 等 means to wait, and 一下 implies that the action will last for only a short period of time, so 等一下 means "wait a second" or "hold on". 等候 and 等待 can both be translated as wait and they can often be used interchangeably, however some collocations are more commonly seen with one word than the other 等候 is usually used with a specific object, for example 等候消息 To wait for a message 等候命令 To wait for orders 等候援軍到來 To wait for reinforcements to arrive 等待 often just means to wait (sometimes blindly), but can also be used with objects 月台上有很多人正在等待著火車的到來 Lots of people were waiting on the platform for the train to arrive 大家目不轉睛地看著發射塔，等待著火箭升空 Everyone gazed at the launchpad, waiting for the rocket to rise into the sky 同學們靜靜地坐在教室裡等待老師上課 The students were quietly sitting in the classroom waiting for the teacher to start class Laurence