Why does my IPhone Keep Vibrating and Not Charging?

I am having trouble with my phone. The phone is almost a year old, but not quite. The charger is a bit worn, and I'm beginning to wonder if the charger is my problem. I have it on a wall charger by my bed so I can check the time if need be. Here's my issue: it vibrates. A lot. Randomly. And I can't sleep. I'm having problems getting it to stop. I don't know if the connection is weak in the cord, but sometimes it will stop charging, then start again and vibrate. And it'll do this over and over, often it's in really quick succession. I looked online and several people have the same thing. Also, a message/notification will pop up. It says something to the effect of: "Charging is not supported with this accessory." I'm starting to worry about it and wonder if it's killing my phone, because my phone isn't holding a charge. (It just went off about four or five times right now...) My lock button is broken, so I CANNOT TURN THE PHONE OFF. What should I do?

What's the issue, and how can I fix it? My sleep level is low and I need to know if I need to buy another charger. To sum things up, my questions are:

What's causing the vibrations and notifications?

Is this a hardware issue, or a problem with the cord connection?

How much does a new cord cost?

Thanks for looking, and please answer. I need to know whats going on ASAP.

Thanks again,

Username411