1) 'Inform me of' and 'inform me about' are both commonly used, both with the meaning of 'give me information about'.
2) The 'to' is needed in the second usage, yes.
3) 'An oven uses electricity', or even 'is powered by electricity'.
4) 'You should play in that place' - yes, 'in' is used here.
(not a teacher, just a language lover)