My baby had really bad cradle cap for about the first three months. I bought a product from the store that was specifically made for cradle cap. It was in the baby aisle with the shampoos and other products, and it's called something like Cradle Care. It has Winnie the Pooh on the bottle. I'd put it on my baby's head and use a toothbrush to gently loosen the scales. It worked really well, but it leaves a yucky feeling in the hair for a bit, and his scalp was flakey afterwards because it was clearing it all off, but in the end I was really pleased with it.
The red blotches may simply be dry skin. My baby looked like he'd developed a rash so I immediately changed his soaps and detergents. It didn't help. Lotions and oils didn't clear it up either. The doctor told me to use Aquafor or Vaseline on him. After weeks of worry, the Aquafor cleared him up within hours. If it's patchy and rough it could be eczema, though.
I hope that helps. Good luck!!