Yes.
You can control what ends up in Calibre's Tags field in FFF Config personal.ini tab.
In the
[defaults] section, put a
include_subject_tags entry that only contains the metadata entries you want in Tags.
Code:
[defaults]
## This is the default value, copy it in and remove the parts you don't want
include_subject_tags: extratags, genre, category, characters, ships, status
As for put Characters in a custom column, the easiest way is to define the custom column first (Calibre will prompt you to restart), then go into FFF Config Custom Columns tab, locate the custom column you defined and use the drop down to select Characters.
Note that these changes only effect downloads from this point on. If you expect you will continue to add custom metadata configuration, I recommend creating a long text custom column for "FanFicFare Saved Metadata" and configure FFF to use it at bottom of the FFF Config Custom Columns tab.
Then when you download or update a story, the metadata will all be saved in that column and you can use the "Update Metadata from Saved Metadata Column" mode to update your columns without hitting the story servers again.