English "Please": 제발 vs 부탁해

Question

When one wants to say in Korean, "pleeeease", the way we do in English when we might even add "pretty please with a cherry on top", 제발 seems like a common translation of please; however, I mostly hear that used the same as Google suggests (whiny and sarcastic):

I have heard 부탁드립니다 used in a way that seems like an authentic please.

Though my question is really just one question: how does one translate a positive, non-sarcastic please?, allow me to add to the question three slants that help guide answers to what I'm really looking for:

• are there more authentic and/or more cute/innocent ways of saying please?
• am I right in thinking that 제발 is simply rude and better left out of a positive/optimistic conversation?
• are there other ways to say/infer please that I should consider in verbal and/or written communications?

Answer 1

Direct translations of please are 제발 or 부디. Simply speaking, however, do not use 제발 or 부디 in most cases. When you say 제발, you look like making you too lower than the hearer. 부디 is better but heard too old way. Instead, you can use more modest expressions like ~(을)를 부탁드립니다, ~(을)을 해주세요 or many others alike.

Answer 2

• 부탁드립니다/부탁드리겠습니다 will be what you looking for. This is appropriate in almost every single circumstances.

• 제발 is not rude at all, but rather gives one an impression like this - 'The one who is saying '제발' is too desperate that he can do whatever he should, even if what he is going to do may damage his reputation - or anything negative.' This is why Nemo said "you look like making you too lower than the hearer". And I see jick's comment now... his explanation is great.

• Same answer as the first one.