Does the aforementioned hadith regarding the punishment for lying apply to a believer who has habitually lied, or to anyone who has lied? And does it mean that lying is worse than adultery? And can it be said that whoever lies has committed adultery seventy times?

Lying is a reprehensible characteristic, and it is one of the traits of hypocrites. It leads to immorality and hellfire. The most severe form of lying is lying about Allah and His Messenger, followed by lying among people to cause corruption. A liar must repent.

As for the Hadith mentioned in the question, stating that lying is seventy times worse than fornication or that its lightest form is like fornication with one's mother, it has no basis and is fabricated. It clearly exaggerates rewards or punishments. Fornication is more severe than lying in common discourse and is mentioned in the Quran after polytheism and killing a soul. It has a punishment and a prescribed حد (legal penalty) in this world, and a warning in the Hereafter that has no equivalent for lying. However, some types of lying, such as lying about Allah and His Messenger, are more severe than fornication and other major sins. Therefore, the claim that lying in general is more severe than fornication is false.

The Ahadith that deny a believer would lie, such as "Does a believer lie? He said: No, only those who do not believe invent lies," or "Can a believer be a liar? He said: No," are weak and fabricated, and cannot be used as evidence.