1) Turn wifi scanning off. It keeps turning on to look for a signal, then turning off. (It will be scanning when you're on that page, turning it off. What else would you be on that page for, except to select a wifi signal, right? (Some people design things with their minds turned off.)
2) The battery sounds like a tiny dendrite. (
https://www.google.com/search?q=lithium+battery+dendrites&ie=utf-8&oe=utf-8 for more than you ever wanted to know about them.) Basically, there's an inherent fault in the way a lithium battery works - it can "grow" shorts. That drops the voltage (sometimes to 0, sometimes long enough to turn the phone off), then the short blows out like a fuse and th phone is working again.
There's no "fix". The industry is still working on redesigning the chemistry so dendrites don't form. $50 to have a battery replaced? That hurts. But think about cars. If one of those batteries in a hybrid or electric car grows a dendrite, and it's under warranty or extended service contract, someone is out a few thousand dollars. The industry is working
really hard on this, they just haven't come up with a solution yet. (Plugging in the charger blows the dendrite immediately, and since it hasn't drawn the battery down that much, it'll go back to a few percent lower than it was when the dendrite shorted it.)
You really have 2 choices:
Live with it
or
Have replace the battery. You could print out some of the points in some of those articles, as proof that it's a manufacturing defect, and see if they'll give you one free, but I'd still be ready to pay for it.