All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
It is permissible to put a sign on the grave, either a stone, wood and the like, according to the opinion of the majority of scholars . The scholars of the Shaafi'i School of jurisprudence, are even of the view that this is desirable.
Ibn Qudaamah said: "It is permissible to put a stone or a piece of wood as a sign in order to recognise the grave. Imaam Ahmad said: "It is permissible for a man to put a sign on the grave in order to recognise the buried as the Prophet put a sign on the grave of 'Uthmaan Ibn Math'oon . Besides, Abu Daawood reported that when 'Uthmaan Ibn Math'oon was buried, the Prophet ordered a man to bring a stone in order to mark the grave, but the man was unable to lift the stone [as it was very heavy], so the Prophet rolled up his sleeves, lifted the stone and put it at the head of the buried, and said: "This is to recognise the grave of my brother so that I would bury whoever dies of my family next to his grave." [end of the quote of Ibn Qudaamah]
Therefore there is no harm if this sign is at the ground level or raised a span of a hand from the level of the ground.
As regards writing on the grave, then this is disliked according to the view of the majority of the scholars . Jaabir narrated that the Prophet forbade covering the grave with cement, or sitting on it, or erecting on it, or writing on it. [An-Nasaa'i and At-Tirmithi]
So writing on the grave is disliked and this applies to whether the deceased is a man or a woman.
Allaah Knows best.