Given the advances in prenatal medical sciences, they can tell lots of about the fetus.

Armed with this information, lets say, that results from some test suggest a baby stands a good chance to be born with down syndrome, do you believe the pregnant woman should/can abort if she believes it would be beyond her capacity/ability to raise this child?  

Is this good cause?

Do you think a person NOT raising/supporting the child has the right to demand/instruct her to give birth to it, why?

Ok, other birth defects show up on these test, some of severe nature, possible......

Same questions, is she within her right to abort if she feels its just beyond her physical and emotional abilities....?

Why not?

Now lets say the pregnant woman doesn't want a particular sex, like a boy, being raised without a father, etc.....
Is that her right?

Why not?

OK, let say the medical testing finds certain characteristic associated with ambiguous genitalia, is that her choice to abort if she thinks that would cause her physical, emotional stress in her life, rearing a child as such?

Why not?

Thanks.    

Not sure if I understand your answers.....

Are you saying its a moral issue?

Also, are you saying in your opinion that once the fetus is viable, is should not be aborted?

"some test suggest a baby stands a good chance to be born with down syndrome, do you believe the pregnant woman should/can abort if she believes it would be beyond her capacity/ability to raise this child?"

 It should be legal.  It is not my authority to make the decision for her, no different than she, or my local government, should decide if I should have a circumcision.

 There are Ethics Committees in healthcare and social services that provide guidance and decision making for at-risk or abusive medical situations.  I would refer decisions to a program like that.

"Is this good cause?"

 I have no opinion on good or bad cause.  I feel if someone thinks aborting a Down's Syndrome fetus is "bad cause" they can always support groups like National Downs Syndrome Adoption Network.  This would have a higher chance of saving the fetus as many abortions will take place anyway regardless of clinic access.  Saving lives over controlling them might work better.

https://www.ndsan.org/

"Do you think a person NOT raising/supporting the child has the right to demand/instruct her to give birth to it, why?"

 No.  They are making a demand and not contributing to a solution.  This makes them part of the problem, and none of that saves an unborn fetus.  I've seen my fair share of autopsy briefings of young pregnant mothers cutting babies out of themselves, taking pills, blunt impact trauma to their midsection etc. due to being told they must have the baby.  

 None of that saves lives unless you create boarding houses where pregnant females are under constant suicide prevention protocol.

"Same questions, is she within her right to abort if she feels its just beyond her physical and emotional abilities....?"

 She is within her right as long as the law allows it.

"Now lets say the pregnant woman doesn't want a particular sex, like a boy, being raised without a father, etc.....
Is that her right"

 She is within her right as long as the law allows it.

 The question very specifically asks if it is within her right.

 It is.  Are you going to tell me that she can be prosecuted?

 
"If the law allowed me to kill you for a particular reason, is that the end of the story for you?"

 Yes.  We execute people legally.  

 I am not going to have the "is a fetus a human"  is it murder etc. etc. conversation.  I am answering the question posed, as it is posed.