Haha, when I saw this sentence I also had a moment of "wait...is it mangos or mangoes?".
Never mind. That's exactly how we know. आम is the subject of the sentence. So, आम हैं means "mangoes are".
I believe it is हमे because it is the dative case of हम. A more literal translation would be "Mangoes are liked by us".
As for typing in devanagari script, I use andriod devices and windows PCs, and all I had to do was download a hindi keyboard for my device.
Hope this helps.