Hi Nelson
Answers to your questions:
1 yes it should turn on when plugged in
2 there is a circuit between the plug and battery, but it doesn't need the battery to be charged to work.
3 you can get to the internal battery, but it will be more than a kludge http://ifixit.org/blog/5564/kindle-fire-hdx-8-9-mini-teardown/
4 I'm not sure, probably not.
What might have happened is that your battery has failed. It won't take a charge but is also 'shorting' the circuit meaning that the rest of the device isn't getting any power. Maybe a battery replacement will fix it, but it's hard to know.
Good luck
Ian