We play out of Final Cut if we don't have enough time to export. It does not stutter. Go View>External Video>All Frames. We haven't run into any issues doing so.
Never rely on the DJ to play your video. We supply our own projector and of course have the proper connection to the laptop. As far as audio goes, there are 2 options. 1 is house sound, and 2 is going through the DJ. Make sure to figure it out BEFORE the wedding. We tell our clients that they must supply the audio, and we will give them an RCA cord. We also have 1/4" to 1/8", and just in case we pack a 50' XLR to 1/4" for when we aren't near the DJ or the DJ doesn't have the cables.