Qur'an 2:7 says: "Allah has set a seal upon their hearts and upon their hearing, and there is a covering over their eyes"

This refers to the loss of the ability to perceive the truth, especially about matters of the divine, truth, or right and wrong. (It does not refer to physical seeing and hearing, but rather seeing and hearing as metaphorical faculties for understanding. Similarly, the heart here is understood as a spiritual organ which perceives the truth.)

Although the verse attributes the sealing of the heart and ears to Allah, it is generally understood to mean that human beings bring this upon themselves through repeated transgression and obduracy against the truth, or denying the truth for personal gain. For instance, in the time of the Prophet (S), some of his enemies were trying to kill him or torturing the Muslims. Over time, this eats away at the capability of the heart (or other faculties) to perceive the truth, until it becomes blocked.

The verse does not specify who is covering their eyes, only that they are covered, and this suggests that they themselves are drawing blinders over their ability to perceive. (In the time of the Prophet (S), some people did this directly - for instance, plugging their ears when around the Prophet (S); today, some people do this by intentionally only going to media websites which reflect their views and ideologies and refusing to consider that they could be wrong.)

Some people who hold there is a reality to deeds in the unseen world would say that the performance of certain transgressions leaves an impact on the spiritual heart - that is to say, people plug up their hearts (ears, etc) through wrong deeds, just like one might plug up a drain over a long time through running detritus through it and not cleaning it out (through repentance and good acts). 

So it is a matter of cause and effect, or action and reaction, based on our own free will. 

However, Allah is the ultimate doer of all acts and all chains of cause and effect ultimately go back to Allah since Allah is the ultimate power in the universe. Furthermore, all things happen with Allah's permission and within the framework of what the divine decree allows, as well as the physical and spiritual laws of the universe. So for these reasons, the sealing is attributed to Allah. 

As for whether Allah intends for all of us to go to heaven... as one of the few creatures around us with free will, heaven and hell are possibilities for all of us, although we can be certain of Allah's justice, and hope for Allah's mercy and the intercession of the Prophet (S) and awliya (A).