Why is my iPhone glitchy, and the battery is low

So I have an iPhone 5c, with the latest update,

And I've recently noticed my phone has been having some problems. Like it'll go really glitchy and start moving things by itself, like it'll open an app by itself, when I try to type it'll erase what I wrote or type in a different letter, idk what to do.

Also recently my battery will go down to 5% and then die, and when it's plugged in it says it's charging, but then it atill dies,

And when it restores it's back at 5% and eventually dies again.