For tying swivels on I always use a palomar knot, I have use the trilene knot in the past but I like the palomar better. For the leadcore go with the willis knot, its easy to tie and will not fail. Yes, you can tie your braid directly to the dipsy or use a swivel, assuming you are talking about your main line. Anything behind the dipsy should be leader material. It seems odd that you are breaking off that often, make sure your line is in good condition and always try to lubricate your knots before puling them tight. What # test and brand of line have you been using?