1. We think that that is which appears to be.

本句正如网友所言：be之后缺少表语，如果添上一个比较级形容词就可以了，例如：better。

这样，which appears to be better 是表语从句，第一个that 引导宾语从句，第二个that是指示代词，例如，指代疑问概念的the question, the problem 等。

我把句子补充完整后，是这个样子：

We think that the question is which appears to be better.

【翻译】我们认为，问题是哪一种（办法）更好。

2. If I said,"What do you think most Christian religious people believe about what happens to you after you're dead?"

【翻译】如果我说，“你认为大多数基督教教徒对你死后发生的事有什么看法？”

本句是一个条件句，缺少主句。

就这个条件句而言，没有错误。

do you think 是插入语，去掉后：

What do most Christian religious people believe about what happens to you after you're dead?

本句中，What 是believe的宾语，about后面的成分是一个名词性从句含有时间状语从句。about表示“关于；对于”。

What do you believe about...? 句型：你对......有何看法？

3. What do you think are those that are likely to come up in this debate?

【翻译】你认为在这次辩论中可能出现的问题是什么？

do you think 是插入语，去掉后：

What are those that are likely to come up in this debate?

that are likely to come up in this debate 是those 的定语从句。根据定语从句中come up 的含义，those 很可能指代“问题”，然后用that 引导定语从句修饰它。