What I would like is for certain schema fields to be greyed out or disabled for most users, and only editable on a component by administrators. Is it possible to do this?
No, not out of the box.
There were several extensions floating about.
http://yabolka.com/gui-extension-readonly-and-hidden-fields-in-tridion-2011-and-up/ was an original from 2011, with a couple of TREX questions you should be able to get this working (e.g. Readonly fields in Tridion 2013 SP1)
To cut a long story short, you could write an extension that
- takes some way of identifying a field should be read-only (e.g. suffix the name with [Restricted] or something similar *)
- resets the read/write status (disable the field, sets a class to identify it) (e.g. a simple JS script over the page could do this) *
You may also want to consider the use of User Group(s) to manage any specific Editors that should be able to write to that field (and take care of checking if they are in that Group from the JS mentioned above).
 I wouldn't use the XML name as you're stuck with it if you decide to change the status later.
 The main challenges here are (a) covering all different field types (b) supporting the hook into the HTML items - you'll be dependant on the HTML formating to navigate to the element you need