Question: Is it such that the Buddhas and Bodhisattvas only help those who are mindful of them, who pray to them for help with sincere faith?
Answer: Having perfect compassion and skilful means, Buddhas and Bodhisattvas also help those who are not mindful of them, who might not even have faith in them. However, functioning along the law of karma, these ones helped must have enough positive karma to be helped, and enough karmic affinity to be helped by them.
As an everyday human example of being helped without asking for help, one does not always have to ask colleagues for help at work, but if they are helpful and can help, they will help you when they see you needing help. Of course, as above, you need to have enough positive karma to deserve help, and enough karmic affinity with them. Otherwise, even if they are willing to help, there are just no conditions to do so.
This is why we should diligently learn more about Buddhas and Bodhisattvas, and to cultivate right faith and sincere mindfulness of them, so as to connect more deeply with them while accumulating more positive karma. This does not only help us in times of danger and distress, but helps to awaken our Buddha-nature, to emulate their great virtues, and advance to Buddhahood too. However, as there are many Buddhas and Bodhisattvas, while we should have reverence to all of them, sincere focus upon one of them will do as they are interconnected.
How To Understand & Practise Mindfulness Of Amitabha Buddha (Amituofo)
The Unseen Power Of Karmic Affinities
Do Buddhas Help Many All The Time?