Is it permissible to marry the son of my paternal grandmother's husband (i.e., the son of my mother's step-father), knowing that he is a second-degree blood relative and of the same age?

The daughters of your paternal grandfather are permitted to marry the son of your paternal grandfather's wife from another man, as there is no legal impediment. This boy is not their brother. Similarly, the grandchildren of grandmothers (such as the questioner) are also permitted to marry him, based on the Almighty's saying: "And lawful for you are [all others] beyond these, provided that you seek them with your wealth, as married persons, not as unlawful paramours." However, since he is a non-mahram, it is not permissible for the questioner to engage in a relationship with him, and she must observe hijab in his presence until marriage takes place.