I had a similar issue, I cant be bothered pulling the cable apart but I suspect that a generic 2 wire usb "charging" cable wont cut the mustard, it possibly needs to be a 4 wire connection, all be it it only needs two of them to charge
as for your other questions, its all to do with MAGLDR
if the phone is OFF and you plug it in it "should" charge yes, but it wont if you have MAGLDR installed
If the phone is in MAGLDR or the bootloader for that matter, it will charge, all be it the light wont come on.
what isn't clear is if in bootloader or MAGLDR the device is capable of autocut off, ie, turning the charge to trickle charge once full, so my advice is that when charging in bootloader or magldr, only do it for 20 min or so then boot to your OS and continue the charge from there.