Thank you both for your answers.
@Sarat: Doesn't if she could imply the condition if she could help (could as in be able to)?
@Philo: So if I understand correctly, both parts of sentence She will help, if she can (first conditional) backshift the tenses to she would help, if she could because of reported speech?
Also why is She promised to help, if she could variant correct? Is it because reporting verb promise can also have pattern verb + to infinitive and that rule of reported speech can override rules for building conditionals (if + present simple, ... will/won't for 1st conditional)?