Is an 'iddah period obligatory for a woman whose engagement was broken off, knowing that she used to seclude herself with her fiancé, and he used to kiss and hug her?

If it was merely an engagement proposal (khitbah) and the legal marriage contract (aqd shar'i) was not concluded, then you are not obliged to observe the 'iddah (definition) (waiting period). However, if the legal marriage contract was concluded, and there was a valid private seclusion (khalwah sahihah) where intercourse could ordinarily take place, then you are obliged to observe the 'iddah. This private seclusion is not achieved if you could not guarantee that your father would not enter upon you both. You must repent for what occurred in terms of seclusion and legal transgressions between the fiancé and fiancée, and the father must repent for condoning it.