5. The two sides have agreed on the date of negotiations.
双方商定了谈判日期。
还能这样说：
The two sides have set the date of the negotiations.
The two parties have fixed the negotiating date.

6. How does the negotiations go?
谈判进展如何？
还能这样说：
How about the negotiations?
How are the negotiations going?
谚语：
Dog does not eat dog.
同类不相残。

7. The negotiation came to a deadlock.
谈判陷入僵局。
还能这样说：
The negotiations were at a deadlock.
The negotiations have reached an impasse.
应用解析：
at a deadlock 处于僵局，停顿状态；
break a deadlock 打破僵局；
come to a deadlock 陷入僵局，停顿状态，相持不下

8. The negotiations have gone really smoothly.
谈判进展非常顺利。
还能这样说：
The negotiation is successful without a hitch.
The negotiations have made progress smoothly.
应用解析：
give one's hair a smooth 捋一捋头发