Du`a to Strengthen Faith and Get Rid of Whispers
Question

I heard a Hadith which says that a man came to the Prophet (blessings and peace of Allah be upon him) and said: How much I have sinned! And the Prophet (blessings and peace of Allah be upon him) told him: “Say: O Allah, surely Your forgiveness is greater than my sins and I have great hope in Your mercy, so, O Lord, forgive me” – and he told him to repeat it three times. What are the supplications for forgiveness from sins? What are the supplications that will strengthen faith and ward off intrusive thoughts (Waswasah)?
Praise be to Allah.In the answers to questions no. 3177 and 39775 , we have listed a number of supplications having to do with repentance and seeking forgiveness.
Does faith increase and decrease?
Faith increases by doing acts of worship and righteous deeds, and it decreases by committing sins. So whoever wants to increase his faith , let him focus on obeying Allah and let him avoid disobeying Him. What will help him to do that is spending time with righteous people and keeping away from innovators and sinners.
Best means to increase faith
Among the most important means that will help the Muslim to strengthen his faith that are the following:

Offering supplication and asking Allah to make you steadfast in adhering to His religion:

Allah, may He be Exalted, tells us that the people of knowledge and faith say: (interpretation of the meaning):
{[Who say], “Our Lord, let not our hearts deviate after You have guided us and grant us from Yourself mercy. Indeed, You are the Bestower”} [Al `Imran 3:8]
Ahmad narrated in Al-Musnad (23463) that `Aishah (may Allah be pleased with her) said: The Messenger of Allah (blessings and peace of Allah be upon him) often used to say in his supplication: “Ya muqallib Al-qulub thabbit qalbi `ala dinik (O Controller of the hearts, make my heart adhere firmly to Your religion).” I said: O Messenger of Allah, how often you offer this supplication. He said: “Man’s heart is between two of the Fingers of Allah, may He be Glorified and Exalted; if He wills, He causes it to deviate, and if He wills, He causes it to be guided.” At-Tirmidhi narrated it from Umm Salamah (may Allah be pleased with her) and classed it as sound. It was also classed as authentic by Al-Albani in Sahih At-Tirmidhi.
At-Tirmidhi (3599) narrated – and classed it as sound – that Abu Hurayrah (may Allah be pleased with him) said: The Messenger of Allah (blessings and peace of Allah be upon him) said: “Allahumm anfa`ni bima `allamtani wa `allimni ma yanfa`uni wa zidni `ilma (O Allah, benefit me by means of that which You have taught me, and teach me that which will benefit me, and increase me in knowledge).” (Classed as authentic by Al-Albani in Sahih At-Tirmidhi) Whomever Allah increases in knowledge, his faith will grow stronger.
Ahmad (3797) narrated from Ibn Mas`ud (may Allah be pleased with him) that he was in the mosque, offering supplication, and that the Prophet (blessings and peace of Allah be upon him) came in whilst he was offering supplication. He said: “Ask, you will be given,” when he [Ibn Mas`ud] was saying: O Allah, I ask You for faith that does not waver, blessing that does not end and to accompany the Prophet (blessings and peace of Allah be upon him) in the highest station in Paradise, the Paradise of eternity. Whomever Allah gives faith that does not waver is strong in faith, and it will not be weakened by desires or doubts.

Asking Allah, may He be Exalted, for guidance

Muslim (2725) narrated that `Ali (may Allah be pleased with him) said: The Messenger of Allah (blessings and peace of Allah be upon him) said to me: “Say: Allahumma ihdini wa saddidni (O Allah, guide me and make me steadfast).
Muslim (2721) also narrated from Ibn Mas`ud (may Allah be pleased with him) that the Prophet (blessings and peace of Allah be upon him) used to say: “Allahumma inni as’aluk Al-huda wa’t-tuqa wa’l-`afafa wa’l-ghina (O Allah, I ask You for guidance, piety, abstinence and independence of means).”

Offering concise supplications, asking Allah for all that is good and seeking refuge with Him from all that is bad, as Ibn Majah (3846) narrated from `Aishah (may Allah be pleased with her) that the Messenger of Allah (blessings and peace of Allah be upon him) taught her the following supplication: “Allahumma inni as’aluka min Al-khayri kullihi, `ajilihi wa ajilihi, ma `alimtu minhu wa ma lam a`lam. Wa a`udhu bika min ash-sharri kullihi, `ajilihi wa ajilihi, ma `alimtu minhu wa ma lam a`lam. Allahumma inni as’aluka min khayri ma sa’alaka `abduka wa nabiyyuka, wa a`udhu bika min sharri ma `adha bihi `abduka wa nabiyyuka. Allahumma inni as’aluka Al-jannata wa ma qarraba ilayha min qawlin aw `amal, wa a`udhu bika min An-nari wa ma qarraba ilayha min qawlin aw `amal, wa as’aluka an taj`al kulla qada’in qadaytahu li khayran (O Allah, I ask You for all that is good, now and in the future, what I know of it and what I do not know. And I seek refuge with You from all evil, now and in the future, what I know and what I do not know.  O Allah, I ask You for the good that Your slave and Prophet asked You for, and I seek refuge with You from the evil from which Your slave and Prophet sought refuge. O Allah, I ask You for Paradise and for that which brings one closer to it, in word and deed, and I seek refuge in You from Hell and from that which brings one closer to it, in word and deed. And I ask You to make every decree that You decree concerning me good).” (Classed as authentic by Al-Albani in Sahih Ibn Majah)
Asking Allah, may He be Exalted, to renew faith in our hearts. Al-Hakim (5) narrated that `Abdullah ibn `Amr ibn Al-`As (may Allah be pleased with him) said: The Messenger of Allah (blessings and peace of Allah be upon him) said: “Faith wears out in the heart of one of you as a garment wears out, so ask Allah to renew faith in your hearts.” (Classed as sound by Al-Albani in As-Sahihah (1585)

How to rid yourself from whispers
The remedy for intrusive thoughts (Waswas) is to ignore them and turn away from them; to recite a great deal of Quran; to do great deal of righteous deeds; and to call upon Allah, may He be Glorified, and beseech Him to ward off the schemes of the Shaytan from you and to make you steadfast in adhering to the truth.
Du`a to protect yourself from whispers
Supplications that are beneficial in warding off the intrusive whispers of the Shaytan (Waswas) include the following:

Seeking refuge with Allah from him . Allah, may He be Exalted, says (interpretation of the meaning):

{And if an evil suggestion comes to you from Satan, then seek refuge in Allah. Indeed, He is Hearing and Knowing.} [Al-A`raf 7:200]

Asking Allah for protection from it. Ibn Majah (773) narrated from Abu Hurayrah (may Allah be pleased with him) that the Messenger of Allah (blessings and peace of Allah be upon him) said: “When any one of you enters the mosque, let him send Salam upon the Prophet (blessings and peace of Allah be upon him), then let him say, Allahumma iftah li abwaba rahmatika (O Allah, open to me the gates of Your mercy). And when he leaves let him send Salam upon the Prophet (blessings and peace of Allah be upon him) and say Allahumm i`simni min ash-shaytanir-rajim (O Allah, protect me from the accursed Shaytan).” Classed as authentic by Al-Albani in Sahih Ibn Majah.
Seeking refuge with Allah from the incitements of the devils, lest they be present with one:

{And say, “My Lord, I seek refuge in You from the incitements of the devils. And I seek refuge in You, my Lord, lest they be present with me.”}[Al-Mu’minun 23:97-98]

Asking Allah to subdue the Shaytan. Abu Dawud (5054) narrated from Abul Azhar Al-Anmari (may Allah be pleased with him) that the Messenger of Allah (blessings and peace of Allah be upon him) said: “Bismillahi wada`tu janbi. Allahumm ighfir li dhanbi wa akhsi’ shaytani wa fukka rihani waj`alni fi’n-nadiyy il-a`la (In the name of Allah I lay down on my side. O Allah, forgive me my sins, drive away my shaytan, help me to fulfil my obligations and join me with the highest assembly).” Classed as authentic by Al-Albani in Sahih Abu Dawud.

Degree of a Hadith
The Hadith mentioned in the question is an inauthentic Hadith. It was narrated by Al-Hakim in Al-Mustadrak (1944) via `Ubaydullah ibn Muhammad ibn Hunayn: `Ubaydullah ibn Muhammad ibn Jabir ibn `Abdullah told me, from his father, from his grandfather, who said: A man came to the Messenger of Allah (blessings and peace of Allah be upon him) and said: How much I have sinned, how much I have sinned! – he said these words two or three times. The Messenger of Allah (blessings and peace of Allah be upon him) said to him: “Say: O Allah, surely Your forgiveness is greater than my sins and my hope in Your mercy is greater than my hope in my deeds.” The man said it, then [the Prophet (blessings and peace of Allah be upon him)] said: “Say it again,” so he said it again. Then he said: “Say it again,” so he said it again. Then he said: “Get up, for Allah has forgiven you.” (Al-Albani classed this Hadith as inauthentic in Silsilat Al-AHadith Ad-Da`ifah, 9/58)
And Allah knows best.