They will. Remember, they fired Scott Forstall over crap software (mostly Maps, but also reportedly the skewmorphic approach to certain apps like Game Center, and Find my Friends, with that stupid simulated leather and stitching). iOS7 will look different enough without alienating the hundreds of millions of people who use it now. (My prediction)
Nor am I. Although, I predict Apple will "borrow" what they deem the best features from Android, Touchwiz, SenseUI, et al.
This is extremely unlikely. I wouldn't hold my breath, if I were you.
The problem with this is that Apple cannot JUST design a phone for guys with big fingers. Samsung can do it because they've established a line of phones, of which the Note 2 is the "NBA player" phone. Apple, in offering one phone, has to try to make the size acceptable to the most hands and fingers as possible.
You're right. They won't make the phone heavier JUST to make it heavier. That's your personal taste, the weight of the phone. The only reason I could see the next phone heavier would be if they do something with the battery(to augment its life) that requires a bigger one that just happens to make it heavier.