Regarding Feature.xml the "can I" answer depends on the version of SharePoint:
SharePoint 2007: Yes, you can. To install it you must use
stsadm -o installfeature -filename myfeaturedir\myfeature.xml and the feature wont be installed as part of deploying a solution
SharePoint 2010: No, you can't both STSADM and Install-SPFeature requires the filename to be feature.xml
The "should I" answer is always NO.
The Elements.xml name isn't special. It's an attribute of your
<ElementManifest> entries in Feature.xml. When you're having multiple different SharePoint artifacts in you Feature it's very common to name the ElementManist files depending on what they contain.
If your feature only contain a single SharePoint artifact (which I'll recommend) then it's common the just name it Elements.xml as the Feature hopefully describes what's in it.
You mention change it on the server, but hopefully you mean in Visual Studio when developing your WSP solution package. You should NEVER add/change any feature on the server except by adding/upgrading/removing WSP packages