Can fragmin (dalteparin) affect pregnancy?

No. Fragmin (dalteparin) is an anticoagulant or blood thinner that may be necessary in pregnancy to prevent or treat blood clots. It is rated as a category b, does not cross the placenta, and is felt to be safe during pregnancy. It can cause increased bruising, bleeding, or a low platelet count.
Unlikely, but maybe. Fragmin (dalteparin) has not been tested in human pregnant patients. It was safe in rats though. The bigger problem is the benzyl alcohol it is diluted in may be harmful. I would ask your ob-gyn if the dose you may require would have enough of the alcohol to be problematic for you.