Is a woman whose husband abandons her for four months without cause, and who requests a divorce after his repeated abandonment, considered among those cursed by angels, and would that deprive her of Paradise?

A wife is not permitted to request divorce merely because her husband does not contact her while he is traveling. What is obligatory upon him is to provide for her and not to be absent from her for longer than the permitted period. Lack of communication is not considered harm that permits requesting divorce.

As for a wife leaving her husband's house without his permission for other than a necessity, it is forbidden and an act of nushuz (disobedience). Scholars have made exceptions for cases of necessity, such as seeking maintenance when the husband is in financial difficulty, or going to a doctor, or consulting a jurist.

The wife must repent and seek forgiveness from her husband, knowing that the hadith you mentioned about angels cursing a woman who leaves her home without her husband's consent is very weak. However, leaving without the husband's permission is forbidden by other sound proofs. The other hadith concerning requesting divorce without a valid excuse is authentic, and it includes anyone who seeks divorce for no harm.