In this run of teshuvot from a variety of years spanning several decades, Rav Moshe Feinstein deals with issues pertaining to how soon a woman can get remarried. The issues are generally those surrounding children, both those unborn as well as those recently born.
In general, the rule is that a woman has to wait for three months after the end of her previous marriage before entering a new one so that if she becomes pregnant it will be clear who the father is. In this case, asked by Rabbi Ephraim Greenblatt of Memphis, TN, the woman had been separated from her husband for several years yet only now became officially divorced. Rav Moshe ruled that she nevertheless had to wait three months from the time of the actual divorce.
In the second teshuva, Rav Moshe's grandson-in-law Rabbi Shabtai Rappaport asked about a woman whose husband was killed in war (presumably in the Lebanon War, as the question was asked in late 1983). The woman had an infant from that husband (born after his death) and had stopped nursing the child for normal reasons. The woman now met a man and wanted to marry him. Despite the fact that in halacha 24 months are allotted for nursing, with the fear that if a woman becomes pregnant before that she will starve the baby, the fact is that since the baby had stopped nursing on its own (well before 24 months) and since the presence of a husband would provide a stable household for this woman and her children, Rav Moshe permitted her to get married without having to wait until the end of 24 months.
Rav Moshe takes a different approach when it comes to a divorcee. In a case posed to him by Rav Moshe Dovid Tendler, the woman was divorced with an infant, and wanted to remarry before the child turned 2 years old. Since the husband in this case was particularly difficult with regard to paying alimony, and the courts were fairly ineffective in forcing him to do so, Rav Moshe found it difficult to consider this child as being supported by his father (the presumption is that the new husband will not want to support the children of the old one - obviously that can vary from case to case). Rav Moshe ultimately permits her to remarry once the child is 18 months provided that she sees to it that the child is financially provided for and provided that she feels an overwhelming need to get married at that point in time.
In a teshuva written one year later to Rav Shalom Tendler, Rav Moshe addressed a case of a divorcee who had a very young infant and had stopped nursing already so that she could return to work (not far remarriage purposes) and now had met someone interested in marrying her. Rav Moshe permitted her to marry the man, provided that she saw to it that the child would be fully provided for until age 2. The fact that the man was considered to be a positive development for the child played a role in this decision as well.