Firstly, as the previous commenter noted, views of women were complicated during this era. Women were not considered men's equals by Irish society as a whole, though there were some individuals who did see them this way. Women were just being admitted to universities in the last 1800s because it was often believed that they could never be a man's intellectual equal. Victorians had literally believed that a woman who behaved in too mannish of a fashion and tried to push herself too hard physically or intellectually could render herself infertile. This was sometimes tempered by the religious idea that women were purer than men and closer to God in some ways, but that notion also became a prison as it required women to be trapped in the domestic sphere of the home and family. This is part of where the sexual double-standard came into being because society believed that a pure woman did not have sexual desires, she only desired to be the model wife and mother. Ireland's devout Catholicism also caused them to relegate women to the roles they held in Biblical stories. To give a full view of how men viewed women during this era would take too much time, but I think you get a sense of the era.

In more direct relation to your questions, I would like to start by talking about Pearse. Padraig Pearse had a very complex relationship to women and to Catholicism. His politics and his religion were intertwined in his notion that Ireland needed a blood sacrifice to save the soul of the nation. His extreme brand of Catholicism did cause him to view women as being purer, in his written works he often compares women to the Virgin Mary. He did believe that women should be included in the 1916 Easter Proclamation as equals in citizenship, which was progressive for his era and separated him from some of his male contemporaries. He also insisted that the leaders of the 1916 garrisons allow women to take part in the rising. Bear in mind that this does not necessarily mean that he saw women as equals in all other ways. Ultimately, he asked the women to leave their garrisons before the surrender because he feared the site of women being arrested would upset the men. He wanted things to go smoothly and he felt that if men saw the women being arrested, they would take up arms again. This again, suggests that his desire for women to take part in the state was tempered by the notion that women need protection.

The other leaders of the rising were mixed in their opinions of women as well. Women in Cumann na mBan and the Irish Citizen Army had done a lot of dangerous work for the nation, especially where gun-running was concerned, but most men balked at the idea of them being involved in actual combat.

James Connolly was exceptional in that he had a progressive view of women and allowed them to join the Irish Citizen Army on the same terms as the men. Constance de Markievicz occasionally commented on the fact that the ICA had beaten the Russians in being the first military to allow women in its ranks. And, it is worth noting that Markievicz was chosen as James Connolly's 'ghost' or second-in-command. She was not allowed to command her own garrison, but she was second-in-command at St. Stephen's Green under Michael Mallin. She was said to be the best shot in all of Ireland and even taught shooting and gun-related skills to Na Fianna Éireann, which was an all male organization akin to the Boy Scouts, albeit with much more paramilitary overtones.

On the other end of the spectrum, Eamon de Valera, who was commanding the Third Battalion at Boland's Mill, saw women as of little use for the rising. He famously refused to have women at his garrison at all, even though he was defying direct orders by doing so. He later admitted that he was sorry he hadn't let the women in because he had to waste some good men on cooking rather than fighting. De Valera had the most misogynistic views of the leaders, despite his backhanded compliment that women were "at once the boldest and most unmanageable revolutionaries." These views would carry over into his changes to the Constitution in the 1930s, in which he enshrined women's roles as 'wives and mothers' and restricted their duties as citizens.

What is even more interesting is the way that the women viewed themselves. While there were women who felt they should stay out of combat, a number of them were quite eager to take part on equal terms. Margaret Skinnider, a member of the Glasgow Cumann na mBan, actually came over from Scotland to take part in the fighting in Dublin. While it is difficult to say how many women were direct combatants, there were a number of female snipers referenced by the witness statements taken by the Bureau of Military History. It is safe to say that they were all endangered by their work whether they were soldiers, messengers, nurses, or cooks. In fact, one nurse had the heel shot off of her shoe while trying to move a wounded man and another got a bullet through her skirt. As one commentator stated "none of them [dispatch carriers] returned unsuccessful. That was a point of honour with them--to succeed or be killed." All in all, there were 200 women in the Easter Rising and about eighty women were imprisoned in Kilmainham Gaol following the rising.

It is also worth noting that British authorities did not take the women as seriously as their male counterparts. Again, this speaks to the widespread idea that women are the weaker sex and couldn't possibly be revolutionaries. In fact, when Kathleen Lynn brought out the surrender, the British soldiers had a debate over whether they should even accept capitulation from a woman. Documents regarding the women prisoners suggest that the soldiers did not really want to imprison them due to their perceived fragility, but they knew they could not safely release them either. The women actually sang and sassed their captors on their way out, something the men couldn't have done. However, it is also worth noting that the women in prison felt sexually threatened by their male captors who leered at them while they were in the toilet. Being a woman simultaneously allowed them to get away with certain activities, while also leaving female prisoners with fears of sexual violence. The Irish War of Independence and Civil Wars would have similarly complicated sexual dimensions.

Sources

McCallum, Christi. 'And They'll March with Their Brothers to Freedom' Cumann Na MBan, Nationalism, and Women's Rights in Ireland, 1900-1923. 2005. http://etd.lib.fsu.edu/theses/available/etd-04182005-153415.

McCoole, Sinéad. No Ordinary Women: Irish Female Activists in the Revolutionary Years, 1900-23. Madison, Wis: University of Wisconsin Press, 2003.

Ryan, Meda. Michael Collins and the Women in His Life. Dublin: Mercier Press, 1996.

Taillon, Ruth. The Women of 1916: When History Was Made. Belfast: Beyond the Pale Publications, 1996.

Ward, Margaret. Unmanageable Revolutionaries Women and Irish Nationalism. London: Pluto Press, 1995.

_. In Their Own Voice: Women and Irish Nationalism. Dublin: Attic Press, 1995.

By and large, yes, sort of, although not entirely in the 'purer than ourselves' way. Most of the leaders of the military council and the signers of the Proclamation felt that women were best suited to be messengers, cooks, and nurses. This was not necessarily a reflection of 'purity', but of more general attitudes that women were not equal to men in the way that is commonly meant today. That said, there were plenty of exceptions. For example, James Connolly's Irish Citizen Army boasted the highest share of woman fighters of all the factions during the Rising, including but not limited to Countess Markievicz. In addition, there are plenty of recorded instances during the Rising, both in Dublin and elsewhere in the nation, of women insisting on being allowed to actually fight and being permitted to by male officers. I'm away from my bookshelf at the moment, so specific citations and further detail will have to wait a bit, but in the interim I can say that Fearghal McGarry's excellent The Rising: Easter 1916 is the source for all the claims I make in this post.