i thought this is old news https://radiolab.org/podcast/205334-fetal-consequences

This seems like it would be the most probable, unsurprising outcome. Billions of cells growing inside of you into a complex biological mass with prolific stem cell activity are very, very likely to metastasise.

It would take a great deal of convincing to prove to me that it was unlikely or uncommon.

I would expect the mother’s immune system to reject the foreign cells though.

It has to have a mechanism to not attack the fetus while its in the womb. One can imagine how balancing it towards the way of leaving cells behind in the womb leads to higher fecundity than the other way of having the body sometimes attack the fetus.

If I am reading the article correctly, it sounds to me like a lack of immune response in the mother is a core element of their findings.

In mice

I was always curious about the original cells of the parents (or more specifically the molecules forming it). Are they somehow “staying” in the baby?

The sperm cell is absorbed into the egg. The genetic material is taken into the nucleus and the rest of the cell is broken down and absorbed. The egg then turns into a more normal type of cell and starts dividing.

I suppose it's possible that that original cell will break down within the gestation period, but it would be in the center of the foetus and would be reabsorbed.

So, yes, probably