Somebody's ears are burning:

耳朵在燃烧 X

感觉有人议论自己 耳朵发热 √

例句：

I bumped into your ex-wife last night.

我昨天晚上偶然遇到你的前妻。

I thought I could feel my ears burning.

怪不得我好想觉得耳朵发热呢。

Be out on your ear:

被开除了 √

例句：

You have to get it right or you are out on your ear.

你必须把这件事做好，不然你就会被解雇。

With half an ear:

不专心（听） √

例句：

I was only listening to the radio with half an ear, while preparing some food.  

我正在做吃的，没太留心听收音机。