Do I need to send it with my Project file?
Will all of the parameters give errors if it is deleted or moved?
The simple answer is no.
Deleting or moving the actual Shared Parameters File does not cause any immediate errors, unless you try to make a parameter from it again. The information from that file is saved with the main Project rvt file. That means that you do not need to send it with a Project file. If the users at the other end want to edit, add or use it they will either need to get yours or make an exact copy themselves.
Here's a little more explanation...
This goes to show just how good Steve Stafford of Revit OpEd is. This is a 2005 article from his blog (which he wrote on a Sunday).
"...deleting the shared parameter from the shared parameter file (there is no link to the shared parameter file) doesn't directly affect a family or project that already uses it. Only when you remove it from a family or project will it affect the existence of data. Also you won't be able to assign or use the parameter again after it is deleted, since a new parameter by the same name is unique in the world as far as Revit is concerned. "
The rest of the article...http://revitoped.blogspot.com/2005/07/shared-parameters-part-3.html