# When Saul saw David
"When Saul had seen David" or "Earlier when Saul saw David". This (17:55-56) happened before David killed Goliath.
# go out against the Philistine
"go to fight against the Philistine"
# whose son is this youth
"who is this youth's father"
# As you live
This was a way of swearing that what he was about to say was true.