Interlaced video is a legacy transmission and delivery format that is, and this is an over simplification, made up of lines of video. Computer monitors typicallyndont dips play interlaced video accurately.
The audio is cutting out probably because everything isn’t matching up in terms of frame rates and playback, or your hard drive can’t keep up.
There are a lot of variables to narrow down. The first thing I would do is make sure your footage and timeline frame rates and formats match to see if that helps. From there you can make more decisions like editing in a progressive Project and deinterlacjng the video if needed (FCPX can do this easily).
Jeremy