Do ordinary Muslims believe that people go to paradise after committing acts of terror and killing?

Answer 1

No. According to the Holy Qur'an, the killing of one innocent human being (any human irrespective of caste, creed, color, religion, country etc.) in the greatest sin, like killing whole human race. A person who intentionally kills others loses his faith of Islam. Terroristic activities are strictly prohibited in Islam.

Answer 2

Ordinary Muslims believe that people who fight in the name of Islam and Allah are destined to go to paradise; this is the concept of esteshhaad (إستشهاد) or martyrdom. The question is whether or not specific acts of terror qualify as being justifiable on those grounds. Most Muslims worldwide do not believe that terrorism and killing of civilians is something that qualifies under martyrdom. The usual explanations are that (1) suicide is prohibited in Islam, (2) Islam forbids the killing of non-combatants, especially if they are People of the Book, or (3) a Muslim has a duty of loyalty to his country and fellow citizens.

A minority of Muslims disagree and hold that if a suicide bomber kills civilians, this can be a proper form of martyrdom and is acceptable, if he was fighting in the name of Islam. This minority, for example, justifies the Charlie Hebdo Massacres because Charlie Hebdo caricatured Muhammad, insulting him, and justifies the attacks on Jews throughout France as retribution for perceived Israeli injustices against Palestinians.

Please see the Pew Research Polls which show what percentage of Muslims support and condemn suicide bombings of civilians at the link here.