People who killed Imam Hussain were also Muslims. Is that correct? If yes, then didn't they know he was the grandson of their Prophet?

People who killed Imam Hussain were also Muslims. Is that correct?

Yes they were from the Muslims but of course were deviated from the right path.

Nafi’ b. Hilal al-Jamali (a companion of Imam al-Husayn) was fighting on that day, reciting:

“I am al-Jamali. I believe in the religion of `Ali.”

A man called Muzahim b. Hurayth came against him, crying,

“I follow the religion of ‘Uthman.”

Nafi’ replied, “Rather you follow the religion of Satan.”

Then he attacked and killed him.

Source - al-Tabari, Ta’rikh (English translation), vol. 19, pp. 136–7

In another example, we have ‘Amr b. al-Hajjaj, when he approached the followers of al-Husayn, say to them:

“People of Kufa, stay steadfast in your obedience and unity (jama'ah). Do not have any doubts about fighting against those who have strayed from the true religion and have opposed the imam.”

Al-Husayn retorted, “‘Amr b. al-Hajjaj, are you urging the people against me? Are we the ones who have strayed from the true religion, and you the ones who have remained firm in it ? By God! If our souls were taken, and you died with your actions, you would know which of us has strayed from the true religion and who was more worthy to be roasted by Hell-fire.”

Source - al-Tabari, Ta’rikh (English translation), vol. 19, p. 137

Both these examples, and there are so many more, prove that the people who came to battle against Imam al-Husayn were from claimants of Islam.

If yes, then didn't they know he was the grandson of their Prophet?

Yes they did. This is because Imam al-Husayn made sure everyone lined up to kill him knew who he was.

He addressed them on the day of Ashura before fighting commenced. The tone of his voice was so loud that most people heard:

"People, listen to my words and do not hurry me so that I may remind you of the duties you have toward me and so that I may give you reasons for my coming to you.

If you accept my reasons, believe my words and give me justice, you will become happier through that, and you will not have any cause against me. If you do not accept my reasons and give me justice of your own accord as individuals, 'Then agree upon your affair and call your associates. Let not your affair be in darkness to you.' [Cf. Quran 10:71] Indeed my guardian is God, Who sent down the Book. He takes care of the righteous.' [Cf. Quran 7:196].(1)

The Imam continued, "Trace back my lineage and consider who I am. Then, look back at yourselves and remonstrate with yourselves. Consider whether it is right for you to kill me and desecrate my inviolability.

Am I not the son of the daughter of your Prophet, the son of the executor of his will and his cousin, the first of believers in God and the man who first believed in what His Apostle brought from his Lord? Was not Hamzah, the leader of the martyrs, my father's uncle and Ja'far at-Tayyar my own uncle? Have you not heard the Prophet of God's saying concerning myself and my brother: 'These are the two lords of the youths of the inhabitants of heaven'?

"If you believe what I am saying - and it is the truth for, by God, I have never told a lie since I learned that God hated people who told them and that those who opposed Him grieved Him ... If you still regard me as a liar, then there are still to be found people who would tell you the truth if you ask them. Ask Jabir b. Abdullah al-Ansari, Abu Said al-Khudri, Sahl b. Sa'd, Zayd b. Arqam and Anas b. Malik to tell you what they have heard from the Apostle of God concerning myself and my brother. Is this not sufficient to prevent your shedding my blood?

"If you are in doubt about this, do you have the slightest doubt that I am the son of the daughter of your Prophet? By God! There is no son of a prophet other than me among you and among the other peoples from east to west. Tell me, are you seeking retribution from me for one of your dead whom I have killed, or for property of yours that I have expropriated, or for a wound that I have inflicted?"

Dead silence reigned over the whole army and nobody uttered a word.

Source - Tabari, Ta'rikh, II, 329–330