1) The girl singing in the hall is/was my cousin.

=who is /was singing

=who has/had sung

=who has/had been singing

可以改成=who sang (一般过去时）吗？

即The girl who sang in the hall is/was my cousin ?

章振邦语法是分别对应的。即，改为定语从句后，用现在时间范畴的时态对应 is：

is singing, has sung, has been sung （从句）----------- is（主句）

用过去时间范畴的时态对应 was：

was singing,  had sung, had been sung （从句）----------- was（主句）

说明一下，章振邦教授也太节约笔墨和纸张了！为什么这么表达呢？让读者大费心思，而且导致误解！

我给他重新改写一下：

The girl singing in the hall is my cousin.

=who is singing

=who has sung

=who has been singing

The girl singing in the hall was my cousin.

=who was singing

=who had sung

=who had been singing

抛开原句，只看网友的句子：

The girl who sang in the hall is/was my cousin.

请问：is/was 都要吗？如果分别都要，我给你答案：

The girl who sang in the hall is my cousin. （正）

The girl who sang in the hall was my cousin. （误）

2) I feel it to be a rare occasion, occurring as it does only once in many years.

= since it occurs

原句occurring as it does， 也可以将as it does去掉，直接说成occurring only once in many years 吧？

as it does，as it did ：是习语。它的结构实际就是表示方式，意为“in fact, actually”，这也是本义。前者跟现在时连用，后者跟过去时连用。因为它是有语义的，不可省略。原句等于：

I feel it to be a rare occasion, occurring as it does only once in many years.

I feel it to be a rare occasion, occurring actually only once in many years.

I feel it to be a rare occasion, since it occurs actually only once in many years.

说明，章振邦这个句子是描述分词转换从句的。你问的是习语as it does。