In Turkish the words her = every and şey = thing would you put them together, to make everything = herşey or would the be kept apart?

While some people are used to write them together, officially they should be written seperatedly.

The authority on this subject is "Türk Dil Kurumu"
(Turkish Language Institute)

http://tdk.org.tr/yazim/default.asp

Smillarly to "her şey", also "bir şey" should be written seperatedly. But certainly the issue is discussable and the TDK not always is correct in their desicions. Its like writing "every thing" and "some thing".

For instance TDK is suggestiong to write "entelektüel" but I disagree since I think it should be "entellektüel".