How can a Muslim girl who is new to the faith overcome her feeling that God will not forgive her repeated mistakes, and how can she perform acts of worship such as Wudu and prayer secretly in a home that does not provide her with privacy, and is it permissible for her to suffice with a small amount of water for Wudu?

We congratulate you on your acceptance of Islam, and know that Allah accepts the repentance of His servants and rejoices in it. Strive to adhere to Allah's commands and to distance yourself from His prohibitions. Be diligent in supplication and seek righteous companionship. If you fall into disobedience, renew your repentance, perform many good deeds, and do not despair. Strive to perfect your acts of worship and to learn their rulings. If a cup of water is sufficient to wash the limbs for ablution (wudu'), it is adequate and the prayer is valid; the flow of water over the limb is sufficient. If you are in an environment where you cannot perform the rituals of your religion, then seek another place and righteous companionship that will help you learn and become firm in your religion, and seek a righteous husband.