I will try and answer the questions. You can view the H.264 video on FCP 7/X/Adobe Premiere 5 but to view it on other programs like Quicktime, you will need to transcode. You should be able to upload the footage you capture and put it onto your mac using FTP 7/X. not sure about iMovie. Nikon DSLRs use compress us B Frame (not sure about 1 Series). Which means that they compress more than Canon does, which uses P frame, so is able to record more. Of course there are limits to the amount of time a camera can generally record for, the Canon 5Dmk2 famously has problems over heating when recording more than about 11/12 minutes of video, because the processor was not designed for video. This has gotten better on cameras but they are not designed for long usage. I can't tell you the length of time a 32gb card will record. you have to include the frame rate in that 24/25/30, which means 24fps will record less than 30fps. The next generation of DSLRs, with the Exspeed 3 processor will be a lot better at shooting video. than current DSLRs, Just look at the 1 series video ability. Not sure that this is much use, I can't say that I am really an expert in video editing.

Yes, here is the info:
http://www.nikonusa.com/Nikon-Products/Product/Nikon1/V27528/Nikon-1-J1.html#tab-ProductDetail.ProductTabs.Kits

I believe that the widest lens Nikon do for the 1 series currently, is the Nikkor 10 mm f/2.8 Lens

You probably don't have the camera on the right settings. The two important elements of taking a photo are shutter speed and aperture. If you have a fast shutter speed, then you will catch movement better but less light will get onto the sensor, so the photo will be darker. With aperture the larger the aperture example (1.8) the more light that gets onto the sensor, but the more out of focus, areas other than the focused subject become (called bokeh). So a camera with a small aperture (f22) will have a be sharp from though the image but will be darker.

I do not know what type of camera you are using, if it is a compact camera, it will generally have different modes, such as sport. This mode will increase the shooting speed of the camera and generally have a more open aperture, but the images will be darker, especially if you are shooting indoors or at night. In auto mode the camera will compensate for the lack of light by slowing down the Shutter speed, which will cause the blur, as the child moves around or your movement if it is a long exposure.

Other ways you can help is to change the ISO, which will increase the cameras ability to shoot in low light, but will start to increase the amount of noise that you get in the photo. use support when taking a photo with a longer exposure. Shoot where there is a good light source, so the shutter speed does not have to be as fast.

There are several options, Depending on your camera, you could well be able to change your camera settings, to take a photo in monochrome. Also a lot of cameras allow you to edit the photo in camera and make it black and white. Personally I always shoot in colour and change everything in post production. As it allows you to have more control and occasionally you like the photo in colour more but it generally is down to what you want. Some people like to shoot in black and white specifically.

http://support.nikonusa.com/app/answers/detail/a_id/17517/~/approved-memory-cards---nikon1-j1