It's convenient for them to communicate with the outside word that useing mobile phone.

首先use的现在分词是using.word拼错了,应该是world吧.
有点语法错误.动名词是可以作主语.在你的句子当中.真正的主语是 to communicate with the outside world ,而不是using mobile phone.把that using去了,直接用by,这个句子就没语法错误了.
It's convenient for them to communicate with the outside world by mobile phone.那这样用呢？It's convenient for them to communicate with the outside world thatthe students use mobile phone.明显是主语从句，to。。。在这里做目的状语或者using mobile phone is convenient for them to communicate with the outside world。这两种应该也都可以吧第一种显得很累赘，而且语法又问题。第一个句子真正的主语依旧是to communicate with the outside world ，而不是that引导的那个句子。所以不可以用那样的方式。第二个句子基本没有语法错误，可是，them指代不明，不知道说的是谁，所以建议将them改为students会更好。using mobile phone is convenient for students to communicate with the outside world。这样比较好。