cummings17

第二句爭議較少, also用於否定句是多數人都接受的, 上Google可以找到很多例子.

至於第一句, 可以從幾個方面來說明.

1. I called her name over the eighties CD, that she had, playing from her computer.
這樣的格式就如非天使所言:
that在做為關係代名詞時，它的位置不可在逗點之後，即that不可用在"非限定用法"上.

2. 那 I called her name over the eighties CD, which she had, playing from her computer. 呢?
一個句子除了要按照大多數認同的規則(也就是所謂的"文法")來寫, 也必須合乎常理, 否則不是不知所云, 就是顯得古怪.
這種寫法是在補充說明"這CD是她(所擁有)的". 如果把上下文一起看, 就會知道這樣的語意在這裡顯得格格不入. 即使換成理查說的寫法也是一樣.
I called her name over the 18's CD she had(, which is) playing from her computer.
而且如果真的要表達這樣的語意, 也應該寫成:
I called her name over the eighties CD of hers that are playing from her computer. 或者
I called her name over her eighties CD playing from her computer.

3. 我贊成意見欄prisoner的解讀, 只是母語使用者有時不太會說明我們所熟悉文法規則, 所以我大膽代勞一下.
(1)
實際上並不是"省略了it", 而是it已經由關係代名詞所取代.
This is the CD. He bought it last night.
This is the CD that he bought last night. [that = it]
而當受詞的that是可以省略的:
This is the CD (that) he bought last night.
(2)
have這個動詞的用法:
His father had him buy the CD last night.
他老爸昨晚要他買這CD.
如果後面這個動作有持續的特性, 也可以用Ving:
His father had him cleaning the house all day yesterday.

了解上面這個用法, 再結合(1), 就會知道原句其實是這樣來的:
I called her name over the eighties CD.
She had the eighties CD playing from her computer.
I called her name over the eighties CD (that) she had playing from her computer.