I cannot understand the subject exacly of this phrase (DL used in romanization) Wo shi 2002 nian nian de

(this above, I understand, is a date of birth)

Yinwei wo bu tai dong yingwen

Baoqian wo zhi kan de dong DL San ju

(A person showed for me with "DL" and never see this example into a romanization)

Wojia you yang gou
我是2002年生的 or 我是2002年来的

因为我不太懂英文

抱歉我只看得懂第三句

我家有养狗

Your second "nian" in the first sentence may be sheng (生，meaning born) or lai (来，meaning came)

I agree with songyuanyao that "DL" may very well be "di". "Di San ju" is "第三句" which means "the third sentence"