Um, lots of questions.
What your doing is not compositing its editing, final cut is not a compositing package.
Let me understand, you are rendering out parts of your film and making .movs out of the sequence that maya takes out?
Are you rendering out an image sequence or sequences and putting them togeather in final cut to edit?
Final cut pro can retime but its easier if you do it with nesting, ( the versions i have used cant handle image sequences as clips so to speak and just deals the striaght images). To nest a sequence make a project and bring in your image sequence as images which last 1 frame each (you can set that in the settings)
When you do this a project will come up in your bin, if you drag that project into another projects time line it will 'nest' that as a clip as opposed to a bunch of images, you are then free to use speed controls on it and cut it up etc.
The issue with the black sounds like a premuliplication problem, which means that you are brining images with an alpha channel in, tga or tiff? An alpha channel basically is a black and what image that defines where things are or are not and is used for layering things in compositing.
Different programs deal with it in different ways, what it seems final cut is dowing is multiplying the alpha with the rest of the channels straight off the bat, so if somthing is black(masked over) where it should not be in your alpha channel (like your floor?) and then its multiplied by its true color (0 times anything is still 0. it will make everything black / transparent.
I dont know how final cut deals with alphas and im sure the documentation will tell you somthing, to deal with this do a single frame render in maya to check wether the floor is showing up as white if not go to the matterial and set the matt opacity to 1 or white. Or to not bother with alpha channels at all turn them off in the render control ...
or if your rendering with mental ray and want to turn off premultiplication on the image go to your frame buffer tab under mental ray and turn off pre multiplication and use a raw color clip.
I would personally do my retiming in maya, but i allways treat a whole animation as a sequence of shots, so i have a scene per shot usually or per couple of shots but i would allways render the shots out seperately from one another.