I am sorry that you are being subjected to this type of harassment. A personal injury and district attorney or criminal lawyer can best address your concerns. The text messages may amount to terroistic threats. Keep records of the threats and print them out or photograph and print the photographs of the text messages. Consult with the criminal attorney. On the civil side a claim for intentional infliction of emotional distress alone will be dismissed. This claim must come with another basis for liability, such as assault, battery etc.
I strongly disagree with the prior attorney response. There is nothing actionable in a recommendation or statement by the biological father favoring termination of pregnancy during the time that option is lawful. Of course you do not have to comply, but his statement alone does not give you rights to collect money damages. What's more, your former sexual partner has no legal obligation to return your calls, nor any legal obligation to provide you with "moral support." And you can block texts if you find contact with this person upsetting.
If you are "about 6 weeks" pregnant, you have NO factual basis for contending that his failure to return your calls "almost" caused you to miscarry. That is not medically credible, and you cannot anticipate having competent admissible medical evidence to establish that position. If you are making these kinds of factual allegations to this man, then it is not surprising that his response to you treats you as an opportunist trying to take financial advantage of him.
Lawsuits and liability and damages are all founded on the premise of the breach of a legal obligation. Nothing set forth in your post suggests that the man you are hoping to collect money from had breached any legal obligation to you. You will have rights to collect support for the child, of course. The rest of your ambitions for claims against this man are without factual or legal basis -- in my view, based on what you have written here.
My responses to questions on Avvo are never intended as legal advice and must not be relied upon as legal advice. I give legal advice only in the course of an attorney-client relationship. Exchange of information through Avvo's Questions forum does not establish an attorney-client relationship with me. That relationship is established only by individual consultation and execution of a written agreement for legal services.
You may be stressed out, but you do not have a right to be free from stress. He simply has no legal duty to provide moral support. You may feel he needs to pay you for your stress, but he has not done anything actionable. If he stresses you out to the point that communication with him almost makes you miscarry, quit communicating with him.
Having said that, he will have an obligation to provide financial support once the child is born, provided that you retain custody of the child.