Is it permissible to surround a grave with bricks to mark its place due to visitors and animals disrespecting the cemetery, and is it permissible to place a headstone with the deceased's name, date of birth, and date of death?

It has been established in the Sunnah that it is forbidden to plaster graves, raise them, construct structures over them, or build upon them. The Prophet, peace and blessings be upon him, commanded that they be leveled. Therefore, fencing graves is not permissible except out of necessity, such as to protect them from erosion, and only to the extent of the need. What the questioner mentioned is not a necessity that permits construction. It is sufficient to deepen the grave, ensure the earth is properly piled, arrange the bricks, elevate the grave about a handspan, and sprinkle water on it. As for placing a marker with the deceased's name, birth date, and death date, it is disliked by the majority of scholars. However, placing a stone as a marker to identify the grave is permissible.