The first two paragraphs match my experience with my N7. Haven't seen the other problem though.
Ha !
I can now concur with the third paragraph too. Just plugged my N7 in after it has sat without any charge for a few days and it too has gone into that reboot loop when I tried to turn it on in its *early stages of charging.
* I have taken to turning it on it as soon as plugging it into charge, as it appeared to work round the non-charging issue. The non-charging issue being where you'd find it had run itself down again, plug it in, come back several hours later to use it, only to find it hadn't even started charging !
(I used to grade my N7 as "good, but not great", the longer I own it the less good it feels I'm afraid, it is "little" things like this that do the most damage to my estimations of its goodness)