How can one repent and return to Allah Almighty when feeling distant from Him, as if cast out from His mercy, and that the chance of entering Paradise has become slim?

Do not despair of Allah's mercy. Quranic verses call upon those who have transgressed against themselves not to despair of Allah's mercy, for He forgives all sins. Allah calls His servants to turn to Him and submit to Him before it is too late. The Quran is a healing and guidance for the believers. No matter how great your sin, it is covered by Allah's general pardon if you repent and turn to Him. Allah praises those who seek forgiveness for their sins and do not persist in what they have done. More dangerous than sins is despair and hopelessness; so do not despair of Allah's mercy, for despair is a characteristic of disbelievers and those who have gone astray. The door of repentance is always open as long as the death rattle has not occurred, and Allah rejoices at the repentance of His servant and replaces his evil deeds with good deeds. Do not delay repentance, for Allah extends His hand at night to accept the repentance of the sinner of the day, and He extends His hand by day to accept the repentance of the sinner of the night. Have a good opinion of Allah, for He is as His servant expects Him to be, and He draws near to those who draw near to Him. Temporarily set aside questions and doubts and hasten to repent, and remember Allah much so that hearts may be at ease, and recite the Quran, for in it is healing and comfort.