The Church of Jesus Christ of Latter-day Saints is not a Protestant denomination or any other denomination that derives it's roots from the Protestant Reformation.  
 
The Church of Jesus Christ of Latter-day Saints believe that our Church is the Restored Church of Christ which existed in the first century AD.  
 
Protestants reformed Catholic doctrine to make there various denominations, the Church of Jesus Christ of Latter-day Saints claims that Christ restored his Ancient Church through the Prophet Joseph Smith so that it existed exactly today as it did when Christ walked the Earth and called his Apostles.

So Mormonism is neither Catholic nor Protestant. So then I still have the question of is Mormonism a hierarchy?

I went with a Mormon friend to service one day and it happened to be a day that an individual could go up front and protest something about their faith or affirm the strength of their beliefs during a moment in the service. What was that day (or action) called?

Scarlett, 
 
We have a monthly meeting - usually the first Sunday of the month - that is called Fast and Testimony meeting. On that day we fast for 24 hours / 2 meals from food and water. We then voluntarily donate the monies that would have been spent on those meals to the Church to help those in need. During that meeting congregants are allowed on their own volition to get up and share their testimony with the congregation. Fast Sunday is meant to renew ourselves spiritually. We try very hard to keep the sabbath day holy and this is one of the things to help us in our lives.