Based on compulsory precaution, one should not desert a believer for more than three days, even if the latter was wrongful to him. It is sufficient to satisfy this obligation by greeting him (e.g. saying 'salam alaykum'). If the other party insisted on the abandonment, he will become the deserter. This prohibition has three exceptions: First: if the desertion was to forbid the wrong. Second: if the desertion would lead to a benefit that the Sharia recommends, like - for example - if desertion leads to paying attention towards a truth that could remain hidden without such desertion, or similar cases. Third: if the reestablishing the relationship would lead to demeaning oneself. One should be careful in not confusing arrogance and anger with self-demeaning.
It is recommended to recite "Ash hadu Anna Aliyyan Waliyullah" in the Adhan, but not with the intention that it is part of the adhan. It is recommended just like reciting the blessing upon the Holy Prophet (the Salawat) after mentioning his name in the adhan.
If the parents were non-Muslims at the time of conceiving the child, and if the relationship between them was legitimately recognized by their religion, then the child is considered to be from a legitimate birth and can lead the prayers.If the relationship was not religiously recognized in their religion, then he cannot lead the prayers even after embracing Islam.If the parents were Muslims at the time of conceiving the child and the relationship was governed by a religiously-accepted marriage contract - even if it is verbal and not recognized by the state - then the child is recognized as their legitimate child and therefore he can lead the prayers.If there was no such religious contract, then the child is not from a legitimate birth and then cannot lead the prayers.