9. I don't think the responsibility should rest with us.
我认为责任不在我方。
还能这样说：
I believe that we don't take the responsibility.
I believe that we are not responsible for that.
应用解析：
rest one's hope on (upon) sb. 把希望寄托在某人身上；
rest with 取决于

10. You will have to compensate us for the loss.
你必须赔偿我们的损失。
还能这样说：
You must pay for what we lost.
You must compensate what we lost caused by your mistake.
谚语：
No great loss without some small gain.
塞翁失马，焉知非福。

11. We cannot entertain your claim.
我们不能受理你们的索赔。
还能这样说：
We cannot consider your claim as requested.
Your claim cannot be accepted.
谚语：
Don't claim to know what you don't know.
不要不懂装懂。

12. I am here to make a claim of the latest shipment.
我到这儿是来对最近的一批货提出索赔的。
还能这样说：
The purpose I come here is to make a claim of the latest shipment.
I intend to lodge a claim of the latest shipment here.
应用解析：
jump a claim 强占采矿权；
claim sth. back 要回某物，索回；
lay claim to sth. 声称对某事有权利；
stake one's claim to sth. 划归为己有，声称与某事有特殊关联

13. Are we entitled to lodge claim?
我们是否有权提出索赔？
还能这样说：
Do we have the right to make a claim?
Are we eligible to claim?
应用解析：
entitle sb. to sth. 给予某人获得某事或做某事的权利，使某人有资格获得某事