The wiggly thing on her belly is her milk vein. It's the major transport to the udder for blood flow. You really like to see large veins in that area indicating a large milk production.
I'd say she's close as well. I don't think you're feeling anything through the skin, but like mentioned before, easiest thing would be just to lube up, wash her backside and your hands, and slide in. Check things out. See if she's starting her dilating, or hasn't started at all.
Her udder does look like she has had problems with mastitis before, but that shouldn't affect her production now much if caught and treated right away. I would still take a cheese cloth or strip cup and when you milk the colostrum out, milk into a jar lined with cheese cloth. See if it's bloody, off smelling, or has flakes. You have to work her teat plugs out anyway, may as well check for mastitis.
Keep us in touch! Anxious for you bab(ies)y!