1.there remains 相当于there is, remains 是系表动词。比之be动词，更有“剩下，存在”之意。
There remains a still more difficult task for us.
还有一项更艰苦的工作需要我们做。
2.nothing remains to be said. 就已经是个句子了，表示：没什么可说的了。
Now that the problem is solved, nothing remains to be said.
问题已经解决了, 没什么说头儿了。
3.rather than 不是固定搭配doing的，它的意思是“而不是”，“与其说，不如说”，前后成分应该是一致的。
We aim at quality rather than quantity.
我们的目的是重质不重量。
The policy will promote rather than hinder reform.
这项政策将促进而不是妨碍改革。
Most of the time he states rather than conveys, and gossips rather than writes.
大部分时间中，他只是述事不立言，谈论而不写作。
I would describe her as handsome rather than beautiful.
我认为她是健美而不是貌美.
He ran rather than walked.
更确切地说，他是跑而不是走。
She enjoys singing rather than dancing. 她喜欢唱歌，而不喜欢跳舞。
但它也可以当介词用，这个时候，就必须是rather than doing sth了，相当于instead of一般会放在句首。
Rather than staying at home, she went out. 她不是呆在家里，而是出门了。
4. would rather do ...than do是固定结构，因为两个动词都受would的限制，所以必须是原形
We would rather go on with the experiment than give it up.
我们宁愿把这个实验进行下去，而不愿放弃不做。
I would rather be laughed at than quarrel with him.
我宁愿被嘲笑，也不愿和他吵架。
5.spent…in doing 也是固定搭配，要注意的是，spend的主语是人，还有，这个in是可以省略的。如果后面是名词而不是动名词的话，介词要用on，这时的on不可省略。
The old man spent most of his twilight years working on his autobiography.
老人暮年的大部分时间都在写他的自传。
I spent the morning trying to round up the documents I needed.
我用上午的时间尽力搜集所需要的文件.
I spent $ 100000 on that house.
我花了1o万美元买下那房子。
参考资料：句库