1.When a hero is moved to lava and knocked (gain dmg from lava) , where is the last position of the hero token ?

lava ? adjacent space ?
2.When a hero is moved to pit and knocked (gain dmg from pit), where is the last position of the hero token ?

pit ? adjacent space ?
3.When a hero move to pit and knocked , where is the last position of the hero token ?
pit ? adjacent space ?

Generally, hero tokens are placed wherever the hero got knocked out, regardless of the reason. This may be in a pit, or in lava. One of the few exceptions to this is if a hero is defeated by ending his turn in lava , he gets to put his token outside the lava. If he dies by entering the lava (whether by moving or being thrown) he still places his token in the lava where he was defeated.

THX, but when this hero stands and place his figure into this space , will he recive damage again from lava or pit ?

THX, but when this hero stands and place his figure into this space , will he recive damage again from lava or pit ?

Effects from terrain or (most) monster abilities like 'Aura' only trigger when you enter the space. So if you start your turn on a lava space you don't suffer damage because you didn't enter that space (you were already there). This is also important for other game effects like crowd control abilities like the Ettins 'Throw' ability because you do enter the space the Ettin throws you in. But then you enter (haha) a whole other realm of complex rules:p