Can Women Offer Janazah Prayer?
Question

Could you please back this up with the hadith to make things clearer and also please try to give full reference of the hadith to everything you state ?
(But with regard to the prayer (women praying the funeral prayer), there is nothing wrong with that. Women may join the funeral prayer. The prohibition applies only to visiting the graves. Women should not visit graves according to the more correct of the two scholarly opinions, because of the hadiths which indicate that that is forbidden. She does not have to offer any kaffarah, all she has to do is repent.)   
Can you tell me if women prayed Funeral Prayers in the times of our Prophet (peace and blessings of Allah be upon him)?
Praise be to Allah.Can women offer funeral prayer?
Praying the janazah (funeral) prayer is prescribed for both men and women . The Prophet (peace and blessings of Allah be upon him) said: “Whoever attends the janazah until he offers the prayer will have one qirat (of reward), and whoever attends until (the deceased) is buried will have two qirats.” It was said, “O Messenger of Allah, what are the two qirats?” He said, “Like two great mountains,” meaning, of reward. (Sahih – agreed upon)
Are women allowed to follow the funeral procession?
But women should not follow the funeral procession to the graveyard, because they are not allowed to do that. It was reported in al-Sahihayn that Umm Salamah (may Allah be pleased with her) said: “We were forbidden to follow the funeral procession but it was not made absolute on us.” (Muslim)
But women are not forbidden to offer the janazah prayer, whether it is offered in the mosque, in a house or in a prayer-place. Women used to offer the janazah prayer with the Prophet (peace and blessings of Allah be upon him) in his mosque and after his lifetime. 
Are women allowed to visit the graves?
Visiting graves , however, is something which is only for men, as is following the funeral procession. The Messenger (peace and blessings of Allah be upon him) cursed women who visit graves. The reason for that – and Allah knows best – is that there is the fear that if women were to follow funeral processions to the graveyard or visit graves , that would cause fitnah (temptation) to others or to themselves. The Prophet (peace and blessings of Allah be upon him) said, “I have not left behind any fitnah more harmful to men than women.” (Sahih – agreed upon). And Allah is the Source of strength.
And Allah knows best.