Yes, God will forgive and save anyone who truly repents of their sin. In some cases, they may have to confess it to a priest in the sacrament of Reconciliation, but God will always receive a repentant sinner back.
God does not "curse" someone for being bad. Sometimes, He may allow someone to suffer the consequences, both natural and spiritual, of their sins to bring them to repentance and discipline them, but He does not "curse" them as if He were malevolent or wished us evil. God "desires all men to be saved and to come to the knowledge of the truth." (1 Timothy 2:3-4, RSV2CE).
12 4 In your struggle against sin you have not yet resisted to the point of shedding your blood. 5 And have you forgotten the exhortation which addresses you as sons? —
"My son, do not regard lightly the discipline of the Lord, nor lose courage when you are punished by Him. 6 For the Lord disciplines him whom He loves, and chastises every son whom He receives."
7 It is for discipline that you have to endure. God is treating you as sons; for what son is there whom his father does not discipline? 8 If you are left without discipline, in which all have participated, then you are illegitimate children and not sons.
(Hebrews 12:4–8, RSV2CE)
Also, our sins have a negative spiritual effect on us that requires painful cleansing; Scripture says,
3 11 For no other foundation can any one lay than that which is laid, which is Jesus Christ. 12 Now if any one builds on the foundation with gold, silver, precious stones, wood, hay, straw — 13 each man's work will become manifest; for the Day will disclose it, because it will be revealed with fire, and the fire will test what sort of work each one has done. 14 If the work which any man has built on the foundation survives, he will receive a reward. 15 If any man's work is burned up, he will suffer loss, though he himself will be saved, but only as through fire."
(1 Corinthians 3:11–15, RSV2CE).
So on the Day of Judgment our works will be tested, and the bad works will be burnt up with fire (which will entail much pain and suffering) and the good works will remain, but we shall be saved — if we have repented of our bad works.
Another thing to keep in mind is that this life is a battlefield between spiritual forces of good and evil. Satan and the other demons are constantly tempting us, and if we consent to the temptations, we are voluntarily enslaving ourselves to the demons. This can feel like a curse, but it's something we bring about ourselves, not something God does. (He simply, with sadness, allows us to have what we want.) "The wages of sin is death." (Romans 6:23). The more we do bad, the more we are held hostage by the demons, and the more we become like them.
The solution is to cry out to God for forgiveness, receive the Sacrament of Reconciliation, and turn our wills towards obeying God and doing good. We become slaves of whomever we obey. (See Romans 6:16 and Romans 2:6-8.) God will always receive us joyfully when we repent; see the Parable of the Prodigal Son (Luke 15:11-32).
Satan is a harsh taskmaster, and he is very possessive. He will take advantage of whatever dominion we voluntarily grant him by committing sin or "being bad" as you put it. He does not want to let go. God is a gentleman, which means that if we are enslaved to sin and Satan, we have to obey God a lot to truly become 'slaves of righteousness' and be freed from Satan. Christ is there to set us free and work with us on this, if we turn to Him and repeatedly renounce Satan and renounce sin (being bad).
Like I said, God will forgive anyone who repents and turns away from their sins, intending to avoid them in the future. The only "unforgivable sin" is refusing to accept God's Mercy and refusing to repent of one's sins at the end of one's life.
The good news is,
3 16 For God so loved the world that He gave His only-begotten Son, that whoever believes in Him should not perish but have eternal life. 17 For God sent the Son into the world, not to condemn the world, but that the world might be saved through Him."
(John 3:16-17, RSV2CE)
God is love (1 John 4:16), and He loves you and all sinners (as well as the righteous), and sent His Son to die for us so that we might be freed from the powers of darkness and have eternal life.