What to Say When Someone Sneezes
Question

Many Muslims, if they sneeze and someone says “Yarhamuk Allah (may Allah have mercy on you),” say, “Yarhamuna wa yarhamukum Allah (May Allah have mercy on us and on you)” or “Hadana wa hadakum Allah (May Allah guide us and you).”
 How correct is this form? Is it narrated from the Prophet (peace and blessings of Allah be upon him)? What is the correct form that is narrated from him?
Praise be to Allah.Forms du`a when sneezing
Different forms of the sneezer praising Allah and responding to the one who says “May Allah have mercy on you” have been narrated. 
Al-Bukhari (6224) narrated from Abu Hurayrah (may Allah be pleased with him) that the Prophet (peace and blessings of Allah be upon him) said: “When one of you sneezes, let him say, ‘Al-hamdu-Lillah (Praise be to Allah),’ and let his brother or companion say to him. ‘Yarhamuk Allah (May Allah have mercy on you).’ If he says, ‘Yarhamuk-Allah,’ then let (the sneezer) say, ‘Yahdikum Allah wa yuslihu balakum (May Allah guide you and rectify your condition).’” 
Imam al-Bukhari narrated in al-Adab al-Mufrad (5033) from Abu Hurayrah that the Prophet (peace and blessings of Allah be upon him) said: “When one of you sneezes, let him say, ‘Al-hamdu-Lillah ‘ala kulli hal (Praise be to Allah in all situations),’ and let his brother or companion say to him, ‘Yarhamuk Allah (May Allah have mercy on you).’ If he says, ‘Yarhamuk-Allah ,’ then let (the sneezer say, ‘Yahdikum Allah wa yuslihu balakum (May Allah guide you and rectify your condition).’” (Classed as sahih by al-Albani in Sahih Abi Dawud) 
Abu Dawud (5031) and al-Tirmidhi (2740) narrated that Salim ibn ‘Ubayd (may Allah be pleased with him) said: The Prophet (peace and blessings of Allah be upon him) said: “When one of you sneezes, let him say, ‘Al-hamdu-Lillah Rabb il-‘Alamin (Praise be to Allah the Lord of the Worlds),’ and let the one who responds to him say, ‘Yarhamuk Allah (May Allah have mercy on you),’ and let him say, ‘Yaghfir Allahu lana wa lakum (May Allah forgive us and you.” (Classed as da’if by al-Albani in Da’if Abi Dawud)
But he classed it as sahih in Sahih al-Adab al-Mufrad (715) with a mawquf isnad that stopped at ‘Abd-Allah ibn Mas’ud (may Allah be pleased with him). 
Abu Hamzah said: I heard Ibn `Abbas saying when someone said ‘Yarhamuk Allah (May Allah have mercy on you)’ to him: “ ‘Afana Allah wa iyyakum min al-nar, yarhamukum Allah (May Allah save us and you from the Fire; may Allah have mercy on you).” (Classed as sahih by al-Albani in Sahih al-Adab al-Mufrad, 955) 
Malik narrated in al-Muwatta (1800) from Nafi’ that if ‘Abd-Allah ibn ‘Umar (may Allah be pleased with him) sneezed and it was said to him, “Yarhamuk Allah (may Allah have mercy on you),’ he would say, “Yarhamuna Allahu wa iyyakum wa yaghfir lana wa lakum (may Allah have mercy on us and you, may He forgive us and you).” 
Al-Nawawi said in Sharh Muslim: 
“Al-Qadi said: The scholars differed as to how one should praise Allah or respond, and there are varying reports concerning that. It was said that he should say, “Al-hamdu Lillah (praise be to Allah)”, or “Al-hamdu-Lillah Rabb il-‘Alamin (Praise be to Allah the Lord of the Worlds)”, or “Al-hamdu-Lillah ‘ala kulli hal (Praise be to Allah in all situations)”. Ibn Jarir said: He has the choice between all of these. This is the correct view, but they agree that he is enjoined to praise Allah. 
He said: And they differed as to how the sneezer is to respond to the one who says “Yarhamuk Allah.” It was said that he should say, “Yahdikumullah wa yuslihu balakum (May Allah guide you and rectify your condition),” or that he should say, “Yaghfir Allahu lana wa lakum (May Allah forgive us and you).” Malik and al-Shafi’i said: He has the choice between these two options. This is the correct view, and the ahadith which mention them are sahih.”
What to say when you sneeze
In conclusion, the phrases used to praise Allah have been narrated in various forms: 

Al-hamdu Lillah (praise be to Allah)
Al-hamdu-Lillah ‘ala kulli hal (Praise be to Allah in all situations)
Al-hamdu-Lillah Rabb il-‘Alamin (Praise be to Allah the Lord of the Worlds) 

 What to say when a Muslim prays for the sneezer
The phrases used to pray for the one who prays for the ssneezer have also been narrated in various forms:

Yahdikum Allah wa yuslihu balakum (May Allah guide you and rectify your condition)
Yaghfir Allahu lana wa lakum (May Allah forgive us and you)
‘Afana Allah wa iyyakum min al-nar, yarhamukum Allah (May Allah save us and you from the Fire; may Allah have mercy on you)
Yarhamuna Allahu wa iyyakum wa yaghfir lana wa lakum (may Allah have mercy on us and you, may He forgive us and you) 

All of these are sahih and the Muslim may choose whichever of them he wants. 
For more, please see these answers: 103435 , 176607 , and 4058 .
And Allah knows best.