If my opponent blocks this spirit's attack and both spirits are destroyed because their BP are the same, can I exhaust one of my opponent's spirits using the effect on this spirit at this time?

How long does the BP gain from this nexus' effect remain active?

If I summon an ST05-006 Leafwolf using 【Swift】 during one of the flash windows of my first attack on my turn, does my attacking spirit gain an additional 1000 BP?

I control three green spirits at the start of my first attack during my turn so my attacking spirit is gaining 3000 BP from the effect on Sacred Tree Stump City. If two of those green spirits are later destroyed during flash windows of that attack, leaving only one, how many BP will my attacking spirit be gaining from the effect on Sacred Tree Stump City?