Is supplicating to God that He make the supplicant possess the ethics of prophets, or speak to him as He spoke to Moses, or send down angels upon him, or take him as a close friend just as He did with Abraham, considered an transgression in supplication?

There is no harm in supplicating for God to bestow upon the supplicant the character traits of the Prophets, as a Muslim is commanded to emulate them.

However, asking God to grant the supplicant the status of the Prophets, or intimate friendship (al-khullah), or for God to speak to him as He spoke to Moses, or for angels to descend upon him as they descended upon the Prophets – this is an transgression in supplication and exceeding the bounds. This is because these are matters specific to them, and intimate friendship (al-khullah) is specific to the two intimate friends (al-khalilayn), Abraham and Muhammad, peace be upon them.

If, however, asking for God to speak refers to inspiration, or if asking for angels to descend refers to their descent upon gatherings of remembrance (dhikr), then there is no harm in this.