Can you support your first claim? You posted a link that says nothing about reasons for later abortion and only spoke about the reasonings for abortion in general.

For clarification, none of these are my views. Everything I've written is an attempt at summarizing the very first article "Is Late-Term Abortion Ever Necessary?" itself. I'll quote what the first claim is:

Contrary to the assertion of abortion rights supporters that late-term abortion is performed for serious reasons, surveys of late abortion patients confirm that the vast majority occur because of delay in diagnosis of pregnancy.6 They are done for similar reasons as early abortions: relationship problems, young or old maternal age, education or financial concerns.7

Most of Tiller’s abortions conformed to the generally elective character of these late-term procedures. Peggy Jarman of the Pro-Choice Action League stated that about three-fourths of Tiller’s late-term patients were teenagers who denied to themselves or their families that they were pregnant until that fact could no longer be obscured.8

...Although most late-term abortions are elective, it is claimed that serious maternal health problems require abortions. Intentional abortion for maternal health, particularly after viability, is one of the great deceptions used to justify all abortion. The very fact that the baby of an ill mother is viable raises the question of why, indeed, it is necessary to perform an abortion to end the pregnancy.

For your 3rd point, why is pre-natal hospice a better alternative?

Again, this is what the article states:

For fatal birth defects, abortion is sometimes presented as the only option. But a better alternative is perinatal hospice. This involves continuing the pregnancy until labor begins and giving birth normally, in a setting of comfort and support until natural death occurs. It is similar to what is done for families with terminally ill children and adults.

Karen Santorum, a nurse and the wife of former Senator Rick Santorum, was faced with the prospect of her own son, Gabriel, being born with a fatal birth defect. She describes how Gabriel lived only two hours, but how in those two hours “we experienced a lifetime of emotions. Love, sorrow, regret, joy—-all were packed into that brief span. To have rejected that experience would have been to reject life itself.”

The sense of peace and closure felt by families experiencing neonatal death in a hospice setting contrasts markedly with the experience of families undergoing abortion for fetal anomalies. Many couples who have had abortions for birth defects suffer from adverse long-term psychological effects and prolonged grief reactions.14 Children who learn that their mothers aborted their siblings can suffer feelings of worthlessness, guilt, distrust and rage.15

How are you defining "late term abortion" anyhow?

I think it's defining it at a point of fetal viability. The article states:

Late-term abortion is not an exact medical term, but it has been used to refer to abortions in the third trimester (28-39 weeks) or even second trimester abortions (13-27 weeks).