"Please smile for me!"
Translation:Làm ơn cười vì tôi!
"Cho" or "dùm" is better than "vì." No one actually says "vì tôi" for this sentence. As you pointed out "vì tôi" means "because of me." If I'm funny and you smile, then yes, that's vì tôi, but if you actually ask someone to smile for you, it can't be vì tôi.
Also, I noticed that Duo teaches please as "Làm ơn." The problem is that "ơn" is a favor that you will be in debt of. We don't take "'làm ơn" likely. We use "vui lòng" instead, which means "with the happiness within you."
Haha. Vietnamese is indeed complicated.
Mời is please, but a different kind of please. It's an invitation, an offer, to mean "you're welcome to." Mời anh ăn = please eat = you are welcome to eat my food. Basically anything that is yours and you want the other person to have it, you can use "mời" such as "mời anh ngồi = please sit" = you're welcome to sit on my chair. "mời anh vào nhà = please come in" = you're welcome to come into my house. So it's not the same please as "please smile."