I was just doing a little more study regarding Amos 2:1-3, where God brought judgment on Moab for burning the bones of the king of Edom. This is a point where understanding the culture is important. Such burning indicated special contempt, and was thought to deprive the dead of peace in the afterlife. In 2 Kings 23:15-16, King Josiah burned the bones of false priests on the altar at Bethel. In our culture, cremation is not done out of contempt, but simply as an alternative to burial.
Compare 1 Corinthians 14:33-35, where Paul writes that women should remain silent in churches. This was very specific to that culture, and not a rule that is "carved in stone". Unless you believe that women should literally be silent from the moment they step into the church until they leave.
There has been some discussion of "systematic Bible study" on this thread. While I've heard the term, I'm not very familiar with what it looks like. However, if this study of placing so much emphasis on what to do with our bodies after we die is an example of how we are to "systematically" study the Bible, count me out. Personally, I prefer the "inductive" study method, where we ask questions to understand the Scripture. Who is talking? What did he mean? How did the original audience understand it? How does it point to Christ? What impact does this have on my life?
Regarding the last question, I don't believe decisions about burial vs cremation make any difference whatsoever. I've never seen God express His anger on anyone for cremating their loved ones. No curses, no unusual financial problems, no unusual health issues, nothing. Certainly this doesn't affect one's salvation, since we are saved by grace through faith. This seems legalistic and pointless.