Going through your partners phone.

yeah no that doesn't sound like they trust you very much at all. It's one thing to be bord and or curious, but if they're keeping regular tabs on who you're texting than that's something you may wanna talk to them about.

That sounds very unreasonable if they want to search your phone but wont let you near theirs, let alone tell you what they're looking for. I can't help but feel that relationships need trust in order to work, and she really needs to learn to trust you. I'm tempted to recommend locking the phone, but that would risk making them mad and possibly trust you even less. all I can say is just keep trying to get her to understand that she needs to trust you.

Whoa, phones are like diaries these days, you can't go through people's phones no matter how curious you are! Though of course if you're on the phone to someone else all the time while you're with them they will start to wonder I guess - insecurity is a bitch.

Yeah, thats not being very trusting. I wouldnt do that to my SO so I wouldnt want it done to me. He/she is not trusting you. You should speak with them about that or get it dealt with.