I downloaded the DEM data from USGS. It comes with several raster files in .img. I know that a mosaic tool can merge them together. I found a lot of tools in the mosaic toolset.
Which one should I use?
You are on the right track, but you don't want to use the tools in the Mosaic folder. Instead, using ArcToolbox navigate to "Mosaic to New Raster".
Arc Toolbox > Data Management Tools > Raster > Raster Dataset > Mosaic to New Raster
All of the files you are manipulating should have the same cell size because they are all from USGS, but I would double check prior to using the mosaic tool by looking at the properties of each of your layers.