my是形容词性无主代词,using是动名词,my using 就相当于个名词词组,mind后面可以跟名词mind sth.,当然这句话还可以说Do you mind if I use your computer for a while?mind后还可以跟doing形式.
这个题跟The days we looked forward to (came) at last.一样,算是个陷阱题,the email做主语,Jack had looked forward to是定语从句做定语修饰the email,Jack一直盼望的邮件,昨天晚上终于到了,主干部分就是the email came.