The both anime and manga was based of a light novel. Normally when a manga is based off a light novel they are translated or drawn very slowly, meaning that the anime is actually ahead of the manga. This has happened for many animes and manga for example Highschool DxD is the anime is up to the 3rd season but the manga is only up to the start of the 2nd season. I believe the translation of Hataraku maou-sama light novels has just started and you might need to wait a while before the light novel is translated up to while the anime is.
so to answer your questions:
1) The manga is not up to the anime yet.
2) If you wish to read it then I normally recommond mangatank because you can load all the pages at once making it easier to read and load.
3) The manga is not that different from the anime if I can recall there were only a few small differences that I remember. However if you are talking about the Light novel then there is nomally a hugh difference in content as the Light novel would try to explains things clearly that in anime the creators won't have enought time to include, However I have not yet read Hataraku Maou-sama so this might not be true, maybe someone else can answer this. But I would recommend that if you do read the light novel that you start from the beginning.