Is it true that reading ten pages of the Qur’an daily protects one from heedlessness, and is listening sufficient instead of reading, and is there a specific remembrance (dhikr) or deed that protects one from heedlessness?

There is no evidence for the validity of what you mentioned. However, it has been authentically reported from the Prophet, peace and blessings be upon him, that whoever recites ten verses will not be recorded among the negligent. Whoever recites one hundred verses will be recorded among the devout. And whoever recites one thousand verses will be recorded among the Muqantireen (those with abundant reward). Additionally, there are other texts regarding deeds that prevent one from being recorded among the negligent, such as maintaining the two rak'ahs of Fajr and reciting fifty verses at night. The listener to a recitation is not equal in reward to the reciter, and sometimes a less virtuous deed may be preferred.