老师们好，我对no doubt的词性和词性用法有一些疑问。 如下文小说里：

And while people have no doubt put two and two together that I hunt illegally, I don’t want to hurt Gale or Greasy Sae or the butcher or even the Peacekeepers back home who are my customers by publicly announcing they’re breaking the law, too.

其中put two and two together是根据事实推出的意思，这应该是一个动词短语。

have no doubt that..也是可以引导一个同位语。

所以从句的谓语到底是什么？  根据put two and two together是动词短语，我觉得have put是while从句谓语，no doubt在这里做状语。 

那么请问no doubt是什么词性？ 是名词吗？名词为什么可以做状语吗？

同样的牛津里有句：

No doubt she'll call us when she gets there.

此处No doubt又改如何解释呢？