This question covers three topics: 

1 – The age at which a person is considered to be a valid mahram for a woman: 

It was said that with regard to the mahram with whom a woman may travel, he should be a Muslim, male, an adult and of sound mind, and someone whom a woman is permanently forbidden to marry, such as her father, brother, paternal uncle, brother through breast-feeding (radaa’ah), father-in-law, etc. 

2- With regard to being alone with a non-mahram woman (khulwah) (inside the city, i.e., not traveling), this is avoided by the presence of an adult mahram or an adult in front of whom they feel shy. The presence of a young child is not sufficient. Khulwah may also be avoided by the presence of another woman or another man, so long as there are no grounds for suspicion and there is no fear of danger. 

(al-Fataawa al-Jaami’a li’l-Mar’ah, 3/935, 938) 

Al-Nawawi (may Allaah have mercy on him) said (9/109): “If a man is alone with a non-mahram woman, without there being a third person present, this is haraam according to the consensus of the scholars. Similarly, if the person with them is one of whom they do not feel shy because he is young, that does not avoid the forbidden khulwah.” 

Shaykh Muhammad ibn Ibraaheem (may Allaah have mercy on him) said: “The person through whom khulwah is avoided must be an adult; the presence of a child is not sufficient. What some women think, that having a child with her avoids khulwah, is mistaken thinking.” (Majmoo’ al-Fataawa, 10/52) 

3- With regard to women visiting graves, the more correct of the two scholarly views is that visiting graves is not permissible for women. See Question no. 8198 and no. 14522.
We ask Allaah to keep us away from evil, visible or invisible… Ameen.