walking in the street

楼主没弄清楚

walking in the street 是省略了(Sb is/are/was/were)walking in the street是正在进行时

walk in the street是一般时态，比如I like to walk in the street.

看上下文决定啊

当然可以，但是用法不同。
walking 是动名词或者现在分词，而walk是动词原形。请看：
He is walking in the street.他正在街上走。
He likes to walk in the street. 他想到街上走走。