5. Thanks for your confidence and support, and we will be always at your service.
谢谢您的信任和支持，我们将热忱为您服务。
还能这样说：
We appreciate your confidence and support and we will service you in a good way.
We provide satisfactory service for our customers to express our gratitude for your confidence and support.
应用解析：
come to one's support 来支持某人；
give support to 支持，支援；
in support of 帮助，为……辩护证明

6. our object is to further cement trade relations with you.
我们的宗旨是进一步巩固与你们的贸易关系。
还能这样说：
To further strengthen the trade relationship with you is our purpose.
We aim to consolidate the business connections with you.
应用解析：
cement的意思是：水泥；胶结材料；（团结的）纽带；粘结，巩固。

7. I hope that we can expand our business to abroad.
我希望能把业务做到国外。
还能这样说：
I hope we can sell a lot of products overseas.
I wish that we can run business at abroad.

8. I have to write a summary of our monthly report.
我不得不写一下本月汇报总结。
还能这样说：
I have to record a summary of the monthly report.
I need to write a monthly report.
应用解析：
draw up a report 起草报告；
present a report 呈递报告