This app was mentioned in 11 comments, with an average of 2.27 upvotes
That sounds like an app locking up and needing to be killed. Could be anything, sometimes it happens to me if the phone is syncing and I turn off all data connections (or just the one it uses to sync at that time). It can't deal with it and just tries to finish syncing forever.
Get something like this to keep an eye on CPU hogs.
FWIW, I've had the same issues, the strange thing is when using a different cable than the one that came with it ( for instance I plugged my Nexus 7 USB - MicroUSB plugged into the MotoX power brick) I was able to leave it flat and it charged just fine. However, going back to the MotoX cable it had to be angled.
as for the other issues you may need to see what all is running in the background processes. Since you're having issues with it charging double check to make sure that the phone says "plugged in and charging" and not "Plugged in, not charging"
third issue, I'd say maybe pointing to a full wipe, maybe look Watchdog and Battery Widget Reborn I've not used watchdog myself but seen posts using it. Hopefully others will have had more experience with similar issue to help you further if none of these help you out.
TL;DR - YMMV
Try going into the application manager and seeing what's running that could be taking up a lot of resources. Alternatively, checkout the app Watchdog (play store link here) which will tell you when an app is taking up a lot of the CPU, even if it's in the background. Maybe they can help you solve the problem.
There's an option to turn off backgrounded services for each app. You could probably kill all running apps in the background and see if it happens. If it still happens, then I'd try and get an app that identifies services running in the background in that time window.
I'm at work and don't have a lot of time but something like this might come in handy - https://play.google.com/store/apps/details?id=com.zomut.watchdoglite
IF that isn't your cup of tea, then maybe reviewing logs at that time stamp can help?
I recommend aLogCat for this - https://play.google.com/store/apps/details?id=org.jtb.alogcat
Some rogue app is destroying your battery by keeping it awake as evident in your awake bar in your screenshot. It doesn't matter what phone you have, this can plague any android phone. First thing I'd suggest is installing Watchdog https://play.google.com/store/apps/details?id=com.zomut.watchdoglite&hl=en which will monitor your cpu usage etc and see what is going on. See if any apps on there stand out as suspicious to you. Also in your android settings menu application manager, you can scroll over to running and see what's going on in there, to try to track down the app. Also have you disabled any system apps? Disabling incorrect ones can cause issues. And do you have an SD card in your phone? SD cards with a corrupt file on it can wreak havoc on your battery life.
If you don't mind just restarting, your best bet would be to factory reset again from recovery mode, and then run it a day without any apps and see if it wakelocks. If not, start installing some apps and see if one of those is the culprit. It's not the update that is ruining your phone, it is a wakelock, and those can be difficult to pinpoint without root.
Watchdog lite - https://play.google.com/store/apps/details?id=com.zomut.watchdoglite
Will alert you to when apps are misbehaving and give you the option to terminate them.