The doctor said not to worry about the funny shape of my baby's head. But doesn't this cause pressure on the brain?

Yes. If the skull bones fuse too early, a condition called craniosynostosis, this will not get better on its own, and often does require treatment: http://www.Drgreene.Com/qa/craniosynostosis.
No. One of my babies had quite the cone head! during birth, a baby's skull bones may mold to allow passage of the head through the birth canal, which can affect the shape of a baby's skull. Molding is normal and has no effect on the developing brain. Over time, the skull grows and the shape of the head fixes itself. Other causes? More info: http://www.Drgreene.Com/qa/craniosynostosis.
Depends. Consider the brain as encased in bones that float on the outer surface,These have edges that push away from each other while the kids head grows.As long as they are not fused, which produced a ridge you can feel, this continues until the head stops growing. Shapes caused by position in the womb or sleeping do not put pressure on the brain. The shape can improve with position,therapy or a helmet.
No. So-called "positional plagiocephaly" (funny head shape because of molding during pregnancy or from sleeping position after birth) does not in any way affect the brain since the separate bones of the skull move to keep the pressure from rising. Craniosynostosis, or abnormal fusing of these separate bones, can cause a problem if not treated, but this is far less common than plagiocephaly.