Red blood cell
Will probably not. You inherit blood type, but not actual erythrocytes (though the mother's erythrocytes do interact with a fetus).
Will probably not. However, while in the uterus and for the first few weeks outside the uterus the Mother's immune system is effectively the newborn's immune system. While the mother doesn't pass on any myeloid progenitor cells, a disease affecting a leukocyte might also be passed on to the child (HIV).
Skin (epithelial) cell
Will not. You inherit many traits to do with skin (melanocyte activity resulting in melanin concentrations, for instance), but no skin cells are involved in the creation of the fetus.
Neuron from the brain
Will not. Neurons are the last time of cell I'd expect to vertically pass on a mutation, not only because their environment is usually tightly controlled (Schwann Cells, Blood-Brain Barrier, etc.), but also because the fetus will develop the beginnings of its nervous system very early on and I'm not aware of the mother's CNS or PNS interacting with the fetus in any significant way.
Can certainly pass on a mutation as long as the mutation is part of the sperm's DNA. Though the particular gene the mutation exists on may be inactivated, it would still be passed on to the offspring and potential future generations.
Cell from lining of the uterus
I'm not positive on this one. The fertilized egg cell must implant itself in the lining of the uterus, and the landing location eventually becomes the umbilical cord. I suppose it's possible, particularly if the mutation occurs closer to the child's end - like the obliterated artery.
Probably not, though like Cell from lining of the uterus I'm not super positive on this one. Given that the placenta is detached from both the mother and child soon after birth, a mutation in a placental cell that hasn't metasticized won't affect either. However, there may be interactions I'm not aware of.
"Stem cell" is a little vague. The body has many specific types of stem cells, and the fertilized egg itself basically turns into all of the stem cells the developing fetus will ever have. If it's referring to the daughter cells of a fertilized egg, then only the child will have the cancer, as the genetic inheritance is unidirectional (the mother's genome is not modified to resemble the child's in any way).
If someone has better knowledge on the interaction between the fetus and the uterus/mother or can come up with some references, listen to them. It's been a while since I've studied development.