介词后是否可接that从句做介宾只见过介词后加疑问代词或副词引导从句,没见过接that从句的,如I heard about that he left New York yesterday.这句话对吗?

这是对的，that从句做介宾

不可以的。
但是，你可以说
I heard that he left New York yesterday. that引导宾语从句
I heard (what he did yesterday).()=谓语

当然是对的了。

I heard that he left New York yesterday.直接用就可以了，不需要后面加that

介词后面能加从句是没有问题的,但是这个问题其实没有意义,因为这个不是重点
重点是,从句前面的那个动词是怎么用的,如果本身就是个及物动词并且要表达动词本身的意思,就直接加从句；如果是个动词的固定搭配,就必须和介词连用才可以.
比如及物动词的：
I can image that you are very depressed these days.我能想象的到你这几天很沮丧.
固定搭配：
I will figure out that how much we have cost.我会算一下我们的开销.（figure 本身做及物动词意思是认为,figure out固定搭配指计算）

He believe in that every man is born equal.
可以的，上句就是that做介宾。

不对！应将about省去.
介词后是可以接that从句做介宾的。例如：
I don't agree with what you said.