Capture time takes its date/time from the EXIF data in the photo.
Did you check if the date/time in the EXIF data of the photo really are correct? If not, you can correct it: http://help.adobe.com/en_US/lightroom/using/WS57264460-DC72-4a1f-A665-1E90907A9FFD.html
You may be tripping over a longstanding bug -- LR doesn't always properly read the capture time of videos. See this topic in the official Adobe feedback forum for a workaround: Lightroom: Still inconsistent capture date/time for videos. If that is indeed what's happening to you, please add your vote and opinion to that thread to make it more likely Adobe will prioritize a fix.
2. How do you select an individual photo/video to get metadata, such as date/time taken, etc.
In the Library module, make sure Window > Panels > Metadata is checked. Then scroll the right column of panels until the Metadata panel is showing. Now, when you click on a photo in the grid, its metadata will show up in the panel.