hi, glad to help , three basic mistakes in ur sentence . 1 "随着“ means "according" so it doesnt make sense ,it should be "接着 （then) " , 2 missed one measure word ”场 “ for "rain" , 3 "跑一跑 ” is inappropriate , double verbs showing together normally means "try sth "that sort of meaning in Chinese , such as "看一看 （take a look )" " 尝一尝（ have a taste) " etc . so u should just say " 跑进 ” to express "run into ". So the whole corret sentence should be 天突然变黑了，接着下了一场大雨，大家都跑进学校里面了。

Hi! It should be: 可以这样写吗（这样is used before an action if there is one.）.天突然变黑（compeletly right.），接着下起了大雨，大家都赶紧往学校跑去。

天突然变黑了 if u don't want to emphasize the changing, "变" can be omitted here. 随着下了一大雨 "随着" usually means "alone with" =伴随着， should be changed to "接着"(after then) , "一" shoud be omitted here, or changed to "一场"，"下了一场大雨" means the rain is over now, it rained sometimes... “下起大雨”means it began to rain..."下着大雨" means it's raining... as continuous tense 大家都跑一跑去学校里面 "跑一跑去" should be changed to "跑到"， I suggests to change "学校" to "教室"/"教学楼"/"宿舍"，more specific, because "学校" compus is too big, it doesn't make sense.

I know what you want to say. Yes, I'm a chinese. 大家都跑一跑去学校里面。 This is weird. Just like 'everyone run and run to school' 大家都跑去学校里面。 This is better. And I saw the other answer, they also help to you.

I think it's better to say: 接着下了一场大雨