I've had a lot of experience painting different sorts of things so I wanted to share a little of my thoughts! When it comes to painting most plastics model paint should do well. I've used it on PVC plastic, resin and vinyl plastic with good results! You can get really cool metallic model paints too for weapons and armor. If you haven't already, for a very professional and realistic look, try picking up washes. They're more "liquidy" paints that you sort of dab on that naturally seeks the cracks and crevices of your model, adding shadow and depth to it! Personally, I use The Army Painter brand. It's not too expensive and I haven't had a problem with it! Vallejo is also a really good but a little more pricey brand. I've used it once or twice but I'm pretty brand loyal
For my earliest customs, I used Michael's store brand painters acrylics with MSC and they turned out pretty not bad I think!
One thing I highly suggest when it comes to customizing dolls, figures and minis is MSC, or Mister Super Clear. It's made for gundam hobbyists and you spray it on your model to both prep and seal it - basically any water based paint like most modelling paints and acrylics will stick to your models! I'll start with a coat of it, paint, then spray again after painting. The surface it creates for painting after the first spray makes it really easy to paint over old coats, so you can go over any wrong colors or mistakes without needing to strip it. It's not a *needed* supply but gives peace of mind that your paint job won't get damaged, and can turn most plastic surfaces into the perfect canvas!
As for painting the swords, you could use masking tape, saran wrap or paper towel to wrap the cloth areas to protect them from the paint. If you can easily take the cloth off though it never hurts to be safe! When it comes to the cording, I find it best if you have a local craft store to go in person. But maybe I'm just old fasioned
it does help when you can hold it in your hands! Otherwise, you could try measuring the diameter of the current cording using a ruler. Then, a google search or look on amazon with that measurement (something like Xmm diameter cord) shooould be able to bring up some options.!
Hopefully at least some of that rambling helped. Good luck with your figures!