Welcome to Shia Dir.
We believe that:
1.Cursing or insulting Aiesha is absolutely Haram [baned].
2.Yes, we believe that she is the mother of the believers, i.e., other Muslims couldn't marriage with her after the demise of Prophet (s), just like they couldn't marriage with their biological mothers. This belief of us can be found in Sunni authentic books, too.
3. We believe that because Aisha was not infallible, she made different mistakes. According to authentic Sunni books, Aisha frequentely disobeyed the orders of Allah and His Prophet (s). For example, both Sunni and Shia believe that the verse
66:4 was revealed against Aisha and Hafsa [another wife of Prophet, who was the daughter of Uthman, the 3th Caliph of Sunnis]. For another example, Allah ordered the wives of Prophet to stay in their houses [33:33], and Prophet Muhammad (s) warned Aisha not to exit from her house leading a battle against Imam Ali (as) [the first Shia Imam, the 4th Sunni Caliph] . But, she fought against Imam Ali in the time of his Caliphate. Al-Albani, whom Sunnis calls as 'current Al-Bukhari' [Al-Bukhri is the wrriter of the most authentic book of Hadith for Sunnis] has confessed that Aisha made a mistake in this doing (Silsilatul Ahadith As-Sahihah by Al-Albani, V1, P. 854, ولا نشك أن خروج أم المؤمنين كان خطأ من أصله).
4.Unfortunately, some Sunnis think that we believe that Aiesa committed adultery. But this is a big lie and we do not believe in it.
5.We believe that the most blessed of Prophet Muhammad (s)'s wive is Lady Khadija (as).
Best wishes!