Topic: Ruling on a Husband and Wife Recording Videos of Their Intimacy for Themselves

In the situation you have described, a husband and wife recording videos of their intimacy, even for themselves alone, was entirely improper and against ‘Haya’ (modesty). Repenting from it and avoiding it completely in future is obligatory.
However, a mistake on your part gives no one else the right to damage your honour and disgrace you in society. Severe warnings have come in the ahadith against exposing the private matters of a Muslim. The Prophet ﷺ said: "Whoever conceals the faults of a Muslim, Allah will conceal his faults on the Day of Judgement. And whoever exposes the faults of a Muslim, Allah will expose his faults, to the point of disgracing him within his own home." (Sunan Ibn Majah, Hadith: 2546)
It is therefore obligatory upon the person who did this to sincerely repent before Allah and to make every possible effort to remove the videos that were spread.
With this in mind, the answers to your questions are as follows:
1) Yes, a husband and wife recording videos of their intimacy is improper and against modesty. This is especially so in our times, when nothing stored on a phone or similar device is safe from being exposed. Making such videos should therefore be avoided.
2) Yes, every sin can be forgiven through sincere repentance from the heart. After repenting sincerely, one should never despair of Allah's mercy.
3) Circumstances sometimes arise in a person's life that leave them disheartened and distressed. Such times should be turned into a means of self-correction and returning to Allah, so that a person learns from past mistakes, avoids them in future, and strives to draw closer to Allah.
4) It is not possible to know with certainty whether Allah has accepted a person's repentance. However, after repenting sincerely, one should hold full hope in Allah's mercy that it has been accepted. Allah says in a hadith qudsi: "I am to My servant as he thinks of Me." (Sahih al-Bukhari, Hadith: 7505) So place your trust in Allah's mercy and be confident that, Insha'Allah, your repentance has been accepted.
5) Insha'Allah, this difficulty of yours will also come to an end, provided you lift yourself out of despair, place your trust in Allah's mercy, and hold firm with patience.
6) Yes, the person who leaked your private videos and spread them in an attempt to disgrace you in society has wronged you, and taking legal action against them is your right. You may approach the relevant authorities to protect your legal rights.
7) In these difficult circumstances, hold firm with patience, supplicate to Allah abundantly, and make a regular practice of reciting "حَسْبُنَا اللّٰهُ وَنِعْمَ الْوَكِيلُ عَلَى اللهِ تَوَكَّلْنَا" Place complete trust in Allah's mercy and His help.