Is not speaking to sisters or girls in general considered a severing of kinship ties and a sign of a psychological complex, and does it prevent one from entering Paradise? And what is the appropriate way to mend family relationships?

A Muslim should be kind and compassionate, loving his Muslim brothers and his relatives. It has been authentically reported from the Messenger of Allah, peace and blessings be upon him, that he said: "Your smiling in the face of your brother is charity," and he also said: "Whoever wishes to be moved away from the Fire and admitted into Paradise, let his death overtake him while he believes in Allah and the Last Day, and let him treat people as he wishes to be treated."

Therefore, you must mend your relationship with your two sisters and forgive them. If the fault was yours, then ask for their forgiveness and promise them not to cause offense in the future. As for speaking to non-mahram women, it is not permissible except out of a pressing need and with the assurance of no fitnah (temptation).