Can u chain Poison of the Old Man and still have LP? (I guess not, just to be sure)
And what kind of damage is Self-Destruct?

Self-Destruct Button??, there is no damage, it simply ties the game up and that's it.

No...if you use Poison of the Old Man before Self-Destruct Button, then Self Destruct Button resolves first

If you use it after Self Destruct Button, then you would gain/opponent would lose LP and then Self Destruct Button resolves and both players immediately become 0, regardless of LP.

Hes right ya no. Poison of the old man may be quick-play but it cant outrun a trap.
And Self-Destruction Button would just take the lp's away there would be no need so save yourself a card and let it sit there.

Basically...it's a tie either way unless Self Destruct Button is negated.