Question: Do Buddhists have to pray on the first and last day of the seventh lunar month, as many Chinese do?
Answer: For Buddhists, what matters more is the full moon day of the seventh lunar month, which is Ullambana Day, though it is not a hard and fast rule that all prayers have to be on that particular day only. It can be throughout the month too. For Dharma practices, the more there is, the better it is.
More on Buddhist practices on this day be learnt in this article: http://purelanders.com/2012/06/25/general-buddhist-pure-land-practices-during-qing-ming-ullambana