What is the ruling on committing sins alongside acts of worship, without ceasing these sins or repenting from them? Are acts of worship (such as prayer, charity, and fasting) accepted while persisting in sin? Do these forbidden actions nullify good deeds? And has anything been mentioned regarding someone in this situation?

If good deeds outweigh bad deeds, then the person is blessed. If bad deeds outweigh good deeds, then it is according to the will of Allah. Good deeds erase bad deeds, while bad deeds nullify good deeds and remove their reward. So, whoever performs prayer, fasts, or gives charity in the prescribed manner, it fulfills the obligation. However, bad deeds may nullify the reward of obedience. Therefore, a Muslim must be wary of sins and repent from them with sincere repentance, for one who repents from a sin is like one who has no sin.