Also, I thought that I remember hearing something like you can see the
Buddha before you die. If this idea is correct, how does one know
that they have seen the Buddha?
In the story at the beginning of this lecture, the first two brothers
have not experienced nirvana, because they are still experiencing
trishna. The third brother (Buddha) has been awakened and understands
that the reality of the situation is that he is going to die, and is
not afraid of dying like his brothers are. As proof that he has
experienced nirvana, he sacrifices himself to the tiger so that she
and her cubs can live.
As for the other two questions, I would like to know the answers
myself.
By personal experience is meant an experience that you have. The
eightfold path is not a personal experience -- it is a list of
recommendations for how to behave. Changing how you behave can lead
to your having different personal experiences. You need to have a
personal experience of nirvana in order to "find Buddha" (as you put
it), and the way to have this sort of experience is to follow the
recommendations given by the eightfold path.
"seeing the Buddha before you die" means something like "you can
attain nirvana before you die". How do you know whether you have
attained nirvana? That's a good question -- we'll discuss it when we
talk about Zen.