For cutting I use flush cutters, something like this.

I've found split ring pliers to be really useful for digging in there to get things really tight at the end. (I originally got them for actually attaching split rings (aka keyrings) and I actually really like these for making keyrings and attaching charms and such

I'm not sure how to help with the knots coming undone. Are you finishing the ends before you start? Your description of the problem there is a little unclear as I'm not sure if you're talking about the cord fraying (in which case always start with nice clean-melted ends), or if the knot itself is coming untied (a more technical issue that could just need adjustments to the way you hold it and how much initial tightening needs done).