RE: Does CA eat plastic?
Don't worry; that's what CA looks like when it cures on a surface. It doesn't "dry", but hardens.
Are you using thick, thin, or medium viscousity? Looks like thin. When gluing up with CA on porous materials (aka wood) use thick CA. It won't run, and will seal better.
Or even better, use epoxy, as it's a gap filling adhesive. CA isn't designed for use with really porous materials like open-grained wood.