The majority of women do not have a period while pregnant, but some do. The difference is an egg is not released (unless it is superfetation – "Superfetation (also spelt superfoetation – see fetus) is the formation of a fetus from a different menstrual cycle while another embryo is already present in the uterus. When there are two separate instances of fertilisation during the same cycle, it is known as superfecundation." Wikipedia). Superfetation is extremely rare and had occurred only 10 times in recorded history. So, yes it is possible.
In terms of growing, it is your uterus that will expand as your baby grows. How much and when you start to show will depend upon your body type, heredity, and your physical health. If you are tall, sufficient hip width, and are prone to carry your baby nestled in, you may never "show" and will be able to wear the same size clothes even if you where athletic and slim. (This was me). If you are larger, the baby’s growth will often be lost inside and if you are small hipped, you will generally carry out showing quickly. The average would be to have a baby bump around 12 weeks.