My husband and I charge our phones in the same place. If his phone is ringing and he can't get to it, I'll answer it for him. A text might come across, we might read it out loud to the other. We have nothing to hide from each other, so it's no biggie.
Not at all. This only causes disturbances and insecurity. For all you know, you may be taking it the wrong way, regardless of how well you know the person. On the other hand, the other person (not your spouse) may be flirting but your spouse is trying to be friendly and not upset them. Idk. But, no, I think it's wrong.
I wouldn't mind if my spouse/partner looked at my phone. I don't have anything to hide. As long as they don't go through deleting stuff and changing things, I'm fine. If he has a super oober problem with me looking at his phone, then... There's a little "sit-chi-ation" there.... :o