Brand new iPhone 5c with multiple issues

My girlfriend recently got a brand new iPhone 5c, since she has gotten it she's been having constant issues with it. Acorrding to her the issues are:

1) Constant freezing on her.

2) Sometimes sliding to unlock doesn't actually unlock. She has to slide to unlock a second time to get into the phone.

3) When using apps, sometimes it will not register the touch input, such as whatever she tries to click on, it will not click.

She has gone to the Apple store and they restored the phone for her, it was fine for the day then the problems started happening again. After that, she was able to get a brand new replacement phone but yet still gives her the same issues.

Has anyone else expierenced these issues? If not, any idea on what's going on? I've had an iPhone since the iPhone 3G and never had these sort of issues, i'm running out of answers for her.