Can Layout or Column information be accessed from within a Field template?

Yes! The following placeholders are available in each field template:

• [[+layout_id]]: the ID of the containing layout
• [[+layout_column]]: the string reference of the column the field is inserted in

Some other placeholders available on each field that may be convenient include [[+idx]] (an index for the fields in this particular column), [[+unique_idx]] (an index that is guaranteed to be unique across all fields and layouts on the page), [[+layout_idx]] (an index for the layout position).

As of v1.8.3, you can also access layout settings through [[+layout_settings.KEY]].

Find a full list of available placeholders in the documentation.