What is the ruling on a disbeliever touching the Qur’an for the sole purpose of memorizing it and gaining expertise in it, and is this permissible for him while he works with the Islamic Museum and there is no other expert besides him, and is he required to perform ablution for that?

It is not permissible for a disbeliever to touch the Holy Qur’an or to enable them to do so, based on the words of the Almighty: "None shall touch it except the purified." If the majority of scholars prohibit a Muslim who is in a state of ritual impurity from touching the Qur’an, then a disbeliever is even more deserving of prohibition. A Muslim sins if they give the Holy Qur’an to a disbeliever, even if it is for the purpose of memorization or contemplation.