To see if your pages are being served with the cache, it’s quite simple.
1) Make sure “Show debug information” is checked in your settings under the Debug tab.
2) View the source of your page and there should be comments at the bottom. If it says “served by advanced cache” it is working.
If it’s not caching the home page, there could be something adding the DO NOT CACHE constant for some reason, or a plugin that’s buffering something else there. Is there any type of special content, galleries, sliders etc on your home page? I have not ran into this yet, but it is possible another plugin could be breaking the page buffer.