Whatever is used as one word but occasionally you will see it as two. It is used more commonly these days as a casual way of saying "fine, I don't care", like you are giving up an argument. It can be said in a non-agressive way too, but usually it's said with attitude. It can be used to replace the word anything, e.g. take anything you like/ take whatever you like.
Whatsoever is used a lot more in literature and I think it sounds nicer than what ever. It is also written as one word. Traditionally it means something like "anything you want" for example, "She takes whatsoever she pleases", which means, she takes anything at all that she likes. It sounds old-fashioned used in this way.
You can also use whatsoever as a negative, for example "I had no control over the children whatsoever" which means, I didn't have a lot or even a little bit of control over those children. It's a varying quantity, so it can be used as anything, or nothing. You can think of it meaning "-at all"; I had no control at all, I had no control whatsoever.