The 1st precept

[Indrajala]

So, encouraging a woman to get an abortion and them going through with it as a result would constitute a violation of the precept, even though you personally did not carry out the deed yourself.

It all comes down to your intent.

So then, what if you encourage this with good intentions?

You can sacrifice a chicken to Kali with good intentions, but it is still unwholesome because it is conditioned by ignorance. You are directly causing harm to another being, thinking it is a good act. This is action motivated by wrong view.

[Cittasanto]

Hi Modus.Ponens

Now is it only breaking the precept if the person whom you talk to about the advantages of death commits suicide?

no. there are different levels of breaking the precepts. fulfilling one or more of the fulfilling factors but not all is still tarnishing the precept.

If I were to praise the advantages of abortion to a woman facing this choice, and she did made an abortion, would that be a breach of the precept?

Yes. life starts at conception in Buddhism.
but also hiring an assasin or talking another into committing the act is full offence for you. similare to how an executioner is not guilty of a crime and the King inherits the kammic fruit (simplified).

Is it breaking the precept just to speak of the advantages of death without it having the consequence of someone dying?

Yes. this would fulfill one or more of the factors so would tarnish the precept.