Q: custom fields greyed out

I tested with Aperture 3.4.5, and I found that it stores Custom Field info in the Preferences file, whereas the new Aperture 3.5.1 only seems to keep this information in the Aperture library.

Try to remove the preferences (/Users/yourhomefolder/Library/Preferences/com.apple.Aperture.plist) from your user library and then reboot your system and try again to create a new Aperture library.

How to remove the preferences is described here:

          Aperture 3: Troubleshooting Basics

Delete the user preferences

You can resolve many issues by restoring Aperture back to its original settings. This will not impact your image files or your library. To reset your Aperture user preference settings to their original state, do the following:

1. Quit Aperture.
2. In the Finder choose Go to folder from the Go menu.
3. Type ~/Library/Preferences in the "Go to the folder" field. Press the Go button.
4. Remove the "com.apple.Aperture.plist" file from the Preferences folder.
5. Restart your computer if you're using OS X Mavericks.

Note: The locations of your Aperture libraries are stored in the preference file listed above. If you have stored your library outside the default location of  ~/Pictures/Aperture Library, make a note of where the library is before deleting the Aperture preferences file. If you have more than one library, you can bring up a dialog to choose which one to load by pressing Option immediately after you open Aperture.

This is in Aperture 3.5.1, and OS 10.9.1

I'm able to delete custom Fields doing the following: (I included all the screen shots so this could be followed)

First in the Info Tab, 3 custom fields

Select Edit from the menu:

Select Manage Custom Fields:

Select the Custom field you want to remove:

Select the minus button The following pop-up appears (if the field is in use)

Select Delete.