Can a person increase their good deeds while committing major sins such as backbiting, fornication, and theft? And will God accept that from him? And will someone who persists in major sins but whose good deeds outweigh his bad ones enter Paradise?

Major sins do not invalidate all good deeds or prevent their acceptance. However, they may nullify good deeds proportionally when actions are weighed. If a servant's good deeds outweigh their bad ones, they will be among those who receive reward. If their bad deeds outweigh their good ones, they will be among those who receive punishment. Nothing invalidates all good deeds except disbelief (kufr), just as nothing invalidates all bad deeds except repentance (tawbah). The perpetrator of a major sin, if they perform good deeds seeking Allah's pleasure, will be rewarded by Allah, even if they are deserving of punishment. Persistence in disobedience is a cause for a bad ending (su' al-khatimah), and therefore, one must hasten to repent from major sins.