1. Yes, if your father'case does not qualify as concubinage by looking at instances such as the married man brings the paramour in the conjugal dwelling or that they live sexual relationship in a scandalous e.g. he introduce the paramour to the society as his wife. (Look for the definition of concubinage in the revised penal). Note: Mere having a child from another woman does not automatically mean concubinage.
2. There is nothing that the children can file against the legal wife unless she commits anything illegal against the children. Marrying their father is not illegal.
3. Yes, they are safe but your mother should go to court for the inventory of their common properties and the delivery of the properties to which she is entitled to. But you the children are not entitled to the delivery of presumptive legitimes because there was no prior marriage of your parents.
4. The only way to enforce your rights is to go to court. But only those properties that belong to your mother may be separated from the conjugal properties. Any property your father owns at the time of marriage forms part to the community property of the husband and wife.