翻译不是唯一的，只要你按要求正确使用了括号了给出的词或短语，句子符合原意且没有语法错误即可。以下修改仅供参考。

1. Each airplane must be checked out seriously before taking off.

seriously 改为 strictly 或 thoroughly 更好一些。

2. Residents firmly oppose setting up waste incineration plant nearby, because they are concerned about the emission polluting the air.

The local residents firmly oppose setting up the waste incineration plant nearby, because they are concerned about the air-pollution by the plant emissions. 居民和焚烧厂都是特指的，需要定冠词。

3. In this area, the investment of ecological project mounts to several billions.

In this area, the investment in ecological projects mounts to as much as billions of yuan.

investment搭配的介词为in。projects应该用复数。高达...元 as much as...yuan.

4. The dry river way is strewn with big and small stones.

The dry river course is strewn with stones of various sizes.

5. Although the war brought a great loss to this country, the local cultural tradition did not perish.

OK

6. In order to construct modern high buildings, many ancient ethnic buildings had to be demolished.

Many ancient buildings with national characteristics were demolished to build modern high-rise buildings.

7. In the earthquake, the main structures of most houses of poor quality disintegrated.

The main structures of most poorly-built houses disintegrated in the earthquake.

8. He made hard efforts for achieving his goals, but lastly his nice dream vanished.

In spite of his great effort to achieve his goals, his beautiful dreams ended up vanishing like soap bubbles.