That's a pretty low end bike to be buying parts for a la carte.
As far as I can tell that new crank you're looking at needs a BB with a 113mm spindle. You might be able to determine your current BB's spindle length with some calipers, or by removing the BB to look for labeling.
Your front derailer probably doesn't need replacing, unless it's been injured or the bike's been left out in the elements for a few years.