Notebook: how to use it?

It's the first notebook I have and it's Windows Vista based.

If it has the battery then you can stand-by it starting from the state
you left.

If it hasn't the battery (i.e. because I removed to use the AC) then
you can stand-by but if you disconnect it from AC you loose the state
and system asks to restart from an anormal stop. Is it normal?

Okay, let's suppose it's. If you end Windows Vista (instead of
stand-bying it) this shouldn't happen, but it still happens, that is
after reconnect the AC it starts saying something about an anormal
stop.. why? I shut it down!

My final question is: can never disconnect the AC if there isn't the
battery inside the notebook?! :-OO

Mhaxx