Is it permissible to remove a part of a cracked and overlapping nail that does not cause pain but looks strange, and would that be considered altering God's creation?

Removing a cracked nail so it can grow back healthy is not considered altering Allah's creation; rather, it falls under the category of removing a defect and disfigurement, which is permissible in Islamic law. The general rule in these matters is that procedures performed to remove a defect are permissible, unlike procedures performed for cosmetic enhancement, which are not permissible.