Is the money earned by a doctor working in the private sector without informing the government hospital permissible (halal) or forbidden (haram)? And is the money he receives from a grant for not working in the private sector, while he is actually working in it, permissible (halal) or forbidden (haram)?

A private employee's benefits are owned [by the employer] only during official working hours. Outside of these hours, he is free to do as he wishes. As for the issue of the grant, if the granting entity stipulates that it should only be taken by someone who does not work in the private sector, then it is not permissible to take it except under this condition. It is not permissible to resort to deception to obtain it without entitlement.