Based on the agreement,all payments          be made by the end of the month.

may

can

shall

will

考查情态动词。句意：根据协议，所有款项应在月底付清。shall用于法律，条款中表示必须要做的事。故选C项。

I would really appreciate       if you can make time in your schedules to attend my lecture today.

that

it

this

one

考查形式宾语。句意：如果你今天能从日程安排中抽出时间来听我的讲座的话，我将不胜感激。I would appreciate it if/when...如果/当...时，我将非常感激。it 做形式宾语。故选B项。

It was along the Mississippi River _________ Mark Twain spent much of his childhood.

how

which

that

where

此处构成It was...that...强调句式，句中强调了介词短语along the Mississippi River。故选C。

           is reported in the newspaper, the epidemic situation is getting better now in China.

It

As

That

What

考查定语从句。句意：正如报纸上报道的那样，中国的疫情正在好转。分析句子结构可知，空格处引导一个非限制定语从句，先行词是整个主句内容，关系词在从句中做主语，表示“正如”，应用as引导，as 引导非限制性定语从句 ，位置比较灵活，可放在主句前。故选B项。

There's no simple solution          this problem.

of

for

to 

about

考查介词。句意：这个问题没有什么简单的解决方法。此处是短语“

the solution to....的解决方法”，应用介词to。故选C项。