Hmm wow ok, i did not find the keys you use anywhere, must have been lot of guessing work.
From what i can see about reminders is, that they need ID, method and minutes.
And they are somehow an own table that is integrated into the calendar, if i understand this correctly.
I guess i will skip this for now, i can't even guess the command you would need to get the ID of the event you are currently creating.
Maybe even Android just adds the reminders after the event is created.
(Save event -> Create event -> Get ID -> Add reminders).
That would mean, you have to make another call after you saved the current event,
to get the event ID of your last saved event and add the reminders.
There is also everywhere in the documentation mostly starttime, differently capitalized, in every insert for an event.
No clue how you guessed beginTime, not even to speak about the capitalization.
android.intent.action.VIEW might be a good start, users suggested to use the MAX ID to get your last created event, but that is not failsafe they guessed, and i would second that.