the third is the same meaning as the first;
the second sentence is not a good expression ,because it puzzled the listener. it can means
1、I will have an exam after oct.- 我十月份后要参加一个考试。
2、I will have an exam in ten months' time. 我十个月后要参加一个考试。
now ,the difference between "月" and "月份"
you can use “月" instead of "月份" in any case.
if your say do sth in which month, you can use 月份 instead of 月,otherwise,you can't. especially means "how long of the time", for example
right:我需要5个月的时间复习。
wrong:我需要5个月份的时间复习。