AFAIK only macbooks have been designed to bypass battery ( once the charge is 100% ) and directly run on connected power. For other notebooks its best to unplug charger at 100% and connect charger at around 10% to get a longer lifetime of the battery.
I've pulled out batteries out of working laptops to test just that theory - only a 2006 Toshiba P300 shut down, the rest of them (newer, Fujitsu, Dell and HP) ran uninterrupted. Either they switched faster or more likely, ran off the AC all the time. It's just good design...
< 40% is not "too far", it's just outside the optimal standing charge range for battery longevity, which studies have found is 40-80%.
In other words you can use your battery from 100% all the way down to shutdown- but the more time it spends in the 40-80% range, the longer its service life.
No, you can use as much as you want. But Li-ion cells will age faster if you deplete them completely, so it's not the best way to keep your battery healthy.
I've often popped the batteries out of ThinkPad's when they are full and just ran on the wall wart. I don't know if they bypass automatically, but you can certainly just pop the battery out yourself.
