Is the son of adultery considered a brother, is it obligatory to maintain ties with him, and is he considered among the relatives, especially if communicating with him causes major problems?

The child born of adultery is not attributed to your father's lineage, nor is he your brother by blood, nor is he among your kin. You are not obligated to maintain ties with him. Your father must repent to Allah for committing adultery by abandoning it, regretting his action, and resolving never to return to it.