Keep one's ears open:

打開(kāi)耳朵 ×

留心聽(tīng)（看）；密切注意 √

例句：

Keep your mouth shut and your ears open.

多聽(tīng)少講。

Have a word in somebody's ear:

和某人說(shuō)秘密話 √

例句：

When you have time would you come to my office, I'd like to have a word in your ear.  

你有空請(qǐng)來(lái)我辦公室，我想同你私下談?wù)劇?/p>

Couldn't believe my ears:

不敢相信自己的耳朵 ×

不敢相信 √

例句：

I couldn't believe my ears. My boss fired me today.

我不敢相信，今天老板把我解雇了。