This excerpt is taken from Sheikh Hussain bin Mubarak Al-Mosuli's Arabic book Al-Awamir wal-Nawahi, whose Urdu translation has been done by Muhammad Sarwar Gohar Sahib under the title Ahkamat o Mamnoaat.
① It is narrated from Sayyiduna Abu Hurairah رضي الله عنه that the Messenger of Allah صلی اللہ علیہ وسلم said:
إذا أحسن أحدكم إسلامه، فكل حسنة يعملها تكتب بعشر أمثالها، إلى سبع مائة ضعف، وكل سيئة يعملها تكتب بمثلها حتى يلقى الله
"When any one of you improves his Islam, then whatever good he does is recorded from ten times up to seven hundred times. And whatever evil he does is recorded only once, until he meets Allah."
Reference: Bukhari, Kitab al-Iman, Hadith 42. Muslim, Kitab al-Iman, Hadith 205/129.
The phrase "any one of you" linguistically addresses those present, but the ruling is general for them and others, and this is agreed upon. Although there is a dispute regarding the nature of the address; whether it is truly linguistic, legal, or metaphorical.
Reference: (See Fath al-Bari 124/1)
② Sayyiduna Abu Hurairah رضي الله عنه also narrates that the Messenger of Allah صلی اللہ علیہ وسلم said:
المسلم من سلم المسلمون من لسانه ويده، والمؤمن من أمنه الناس على دمائهم وأموالهم
"A Muslim is one from whose tongue and hand other Muslims are safe, and a believer is one from whom people's lives and wealth are safe."
Reference: (At-Tirmidhi, Kitab al-Iman, Hadith 2627)
Imam Tirmidhi رحمه الله said: "This hadith is Hasan Sahih."
Tabarani narrated from Abdullah bin Amr رضي الله عنهما and at the end it says: "A Muhajir is one who abandons evil and avoids it." But its chain is weak because it includes Ru' ibn Salah.
Reference: (Tabarani fi al-Awsat, Hadith 232)
① It is narrated from Sayyiduna Abu Hurairah (may Allah be pleased with him) that the Messenger of Allah (peace be upon him) said:
إذا أحسن أحدكم إسلامه فكل حسنة يعملها تكتب بعشر أمثالها إلى سبعمائة ضعف، وكل سيئة يعملها تكتب بمثلها حتى يلقى الله تعالى
"When any one of you becomes well-established in Islam, then whatever good he does is recorded for him from ten times to seven hundred times, and whatever evil he does is recorded only as it is. Until the person meets Allah Almighty."
Reference: Bukhari, Book of Faith (42). Muslim, Book of Faith (205/129)
② It is narrated from Sayyiduna Abu Saeed Khudri (may Allah be pleased with him) that he heard the Messenger of Allah (peace be upon him) say:
إذا أسلم العبد فحسن إسلامه يكفر الله عنه كل سيئة كان زلفها، وكان بعد ذلك القصاص: الحسنة بعشر أمثالها إلى سبع مائة ضعف، والسيئة بمثلها إلا أن يتجاوز الله عنها
"When a person becomes a Muslim and firmly adheres to Islam, Allah forgives all the sins he committed before (embracing Islam). After that, the system of recompense begins, where the reward for good deeds is from ten times to seven hundred times, and the punishment for evil deeds is only equal to the evil done, unless Allah forgives him."
Reference: Bukhari, Book of Faith (41) Nasai, Book of Prayer (106/8)