Usually I just look at the preview screens in handbrake and see if it needs deinterlacing or not... although I don't think it particularly hurts to deinterlace when you don't have to... some of the hardcore videophiles will say otherwise I'm sure but I can't tell a difference...
It depends. When the DVD is interlaced (TV), you deinterlace. If it isn't interlaced, you don't deinterlace. 😀
In Handbrake, look at a few images in the preview. Interlacing artefacts (mouse teeth) are very visible in any scene with fast motion. Have a look at a DVD with a TV program, so you will know what you are looking for. If the DVD contains interlaced material, then encoding without deinterlacing looks horrible because the source material without deinterlacing looks horrible, and it is much harder to encode, so you get lower quality with the same bitrate. On the other hand, if the source material is not interlaced, then deinterlacing just reduces the quality at no gain at all.