Is it permissible for an engaged couple to communicate via audio and video over the internet and engage in acts that arouse sexual desire?

If the engagement is merely a promise of marriage without a contract, then what you are doing is forbidden and you must repent from it immediately, for the Prophet, peace and blessings be upon him, said: "A portion of fornication has been destined for the son of Adam," and this includes metaphorical fornication such as forbidden glances, touches, and speech. However, if the engagement means that a valid Islamic contract has been concluded, then there is no harm in what you are doing, because you have become his wife. Nevertheless, this should be restricted to ensuring that no one else becomes aware of your private matters or images, in order to avoid harm.