The FL-D filter should be sufficient to approximately compensate for the florescent lighting. However, if you want to provide an accurate compensation, you will need to use the appropriate color compensating filter. I have used a CC30M with "normal" fluorescent lighting with good results. Given that fluorescent lighting varies in color temperature quite a bit, it is best if you can use a color compensating filter instead of a FL-D filter (which offers limited correction). This would also take care of your mixed lighting scenario.
Note: FL-D is for use with daylight film. If you are using tungsten film, you will need FL-B.