Problems with photo stream
I'll try to answer your inquiries based on my experience.


In iOS, to be able to save an image from the Photo Stream (PS), you need to tap an image and select the Save Image action to make a copy of that image to the Camera Roll.
That may be a bug in iOS/OS X, I'm not sure, but that also happens to me especially with the most recent photos I took. But sometimes, after a couple of minutes, the Photos app on my Macbook Air will be updated. You can connect your iPhone to your Mac and just import those images that you can't see in your Photos app.