To clarify, in gmail mine look fine, too. It's when you actually download them from Gmail to your PC that they are suddenly flipped the wrong way, (and also when sending to someone they end up flipped on their end, MMS/e-mail/forum uploads/whatever).
As for the first question...
All three photos show correctly on the phone in my stock Gallery app (Quickpic too). Under details, one of the photos is 0 degrees, the other (despite showing upright correctly right now as I am looking at it) shows 90 degrees, and the third also shows 90 degrees in "details" despite looking portrait.
So the software of the camera is mistakenly adding 90 degrees to the EXIF data I guess. The correct one with 0 degrees is the Google Camera one.
The second question...
I haven't done anything with Google's Photos app on this new phone yet. Not even opened it. Guess I'll give that a try now, too.
Maybish also mentioned she's been using an SD card in hers, while I'm just using the internal storage with no card ever inserted into the device yet. What about you, lostchild?