remember to give the player problems
"First, can a person under the effects of a polymorph spell become pregnant?
Second, Could a person induce pregnancy while under the effects of a polymorph spell?"
Obviously yes in both cases. Under rules - The polymorphed critter gains the "natural abilities" of the new form, which would clearly include doing what comes naturally...
And we do want complications for the PC, which means pregnancy should be a definite possibility.
"If pregnancy is possible under 1 or 2 above, what would happen to the fetus when the spell is reversed? What happens to the child when the pregnancy comes to term?"
1st point is that the PC won't know, and should be quite worried about the worst [however defined by the PC] happening.
The DM should likely rule according to what keeps life most interesting for the PC. This means the kid is still there in most cases. [A male polyed to female and becoming pregnant should still be pregnant, with both father/mother and child in danger unless they gain some magic aid. As a technical point, a man can give birth, with the assistance of a few million$ in highly skilled doctoring, who preferably have tried this about a dozen times before to work out the kinks. Those of us who are not insane billionaires of course prefer the more regular methods.] Most likely the child appears a normal member of the mother's race, but some odd points will start to appear. Where the DM wants a quest for magic correction, the child should be born the wrong race or of mixed race.
"Third, what happens to an existing fetus when Polymorph is cast onto someone who is already pregnant?"
Here again, eliminating the child is too dull. So the kid survives the experience, with complications. The kid would be an apparent member of the mother's apparent race when born. Whether she is currenly polymorphed or has been changed back, there will be signs that there is something odd about the kid.
"Fourth, what if the form the person is polymorphed into is of a different Type than that of the persons natural form. For example, a humanoid is transformed into a giant or a dragon."
The standard rule of fantasy is that 1 [female] + 1 [male] = 3. The race of either parent is not important. One prefers the same race, but successful mating with just about any other is entirely possible. So our humanoid/dragon can get kids by either race, or by a 3rd, tho the polymorphed will likely prefer the old race who will reject him/her while he/she may be sought by members of the new race despite his/her disinterest in the idea.