1. Yes. Depends on the reason of the infertility though. There are some genetic disorders where the reproductive organs fail to develop properly which results in the person being unable to menstruate. These are very, very, very rare. Largely, infertility will be because of a problem with your eggs (they might not be released from the ovary or they might not be normal). That doesn't effect the way in which your hormones work. Your body will still line the uterus with blood regardless of whether there is an egg there to work or not.
2. Definately not true. That's like saying you will grow longer arms by pulling on them a lot. Doesn't work that way!