I have had my Asus T-100 for over a year and I've had a few of the frustrations mentioned. There seems to be an issue with the battery charging circuit when the laptop is in sleep mode. I always shut it down after I use it and it charges up OK these days (but slowly). Another little trap I've found is that the charger is in two pieces and can slightly pull apart while still appearing fine -just need snap it back together.
I did update the BIOS a few months ago and that seemed to help with the random shutdown at about 30% charge.
I love this little guy now, and sometimes I remove the keyboard for weight and take it on my bike with me.
Good to know where the home key is too -might come in handy :)
Cheers all ...best of luck,
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