A political group of people
no
The Muslim Brotherhood.
Egypt
It is against the Egyptian constitution for any religious gathering or party to rule Egypt. Accrordingly, even if people belonging to the Muslim Brotherhood govern Egypt, they will be subject to the Egyptian ruling system and subject to their own claimed religious Agenda. On the other hand, Muslim Brotherhood is not of so much popularity in Egypt to win enough majority to rule Egypt.
Most Westerners do not really have an opinion on the Muslim Brotherhood. Those who aware of what happened in Egypt in 2012, when the Muslim Brotherhood took over Egypt and tried to impose Islamic Law rather than make important changes to improve the economy, have a rather negative view of the Brotherhood. Those who know that Hamas is the Palestinian branch of the Muslim Brotherhood and that the Muslim Brotherhood is trying to equate criticism of Islam with bigotry against Muslims as people have an increased level of revulsion towards the organization.However, there are Westerners who support the Muslim Brotherhood seeing them as "Moderate Islamists", even though none of their political positions are actually moderate.
To make the country better and fairer to free palestine
The Arab Socialists and the Muslim Brotherhood wanted to end foreign domination in Egypt. In 1952, Colonel Nasser of the Arab Socialists had enlisted the help of the Muslim Brotherhood to help overthrow the Farouk regime. Once Colonel Nasser was elected President, and Egypt emerged as an independent nation, the radical differences between Colonel Nasser and his allies on the one hand and the Muslim Brotherhood led to open conflict.
Muslim Brotherhood was created in 1928.
No, this is a myth. There is no evidence he ever did any such thing.
There have been several fundamentalist Islamist regimes such as the Taliban in Afghanistan, the Ayatollahs in Iran, and the Muslim Brotherhood in Egypt.
No
The Muslim Brotherhood hated Mubarak because he never wanted them to be involved in politics, even when 20% of the people voted for them. Mubarak also never really took corrct care for his people and did not give them fair pay, enough jobs or enough freedom. Mubarak also accused the Muslim Brotherhood for stirring trouble in the past, blaming them for starting a fight. Obviously, this is not the case because it all comes to Mubarak's decision in controlling Egypt, NOT the Muslim Brotherhood.