1) I believe both Goliath and Delilah would stay in battle.
Delilah would definitely stay in battle because she wasn't banded in, so no amount of negating will stop that. I could see Goliath being kicked out of battle, but only because exchange is a weird ability, Goliath negates the band, which originally targeted Philistine Armor Bearer and some properties follow as characters are exchanged (In T2 if you are attempting to rescue a Lost Soul and it gets exchanged you can rescue the exchanged Lost Soul that now occupies the same game space (or whatever we call it) as your original target, so in that sense I could see Goliath kicked out of battle... I just don't think that's the current rules.
2) The draw would be negated because Goliath isn't limited to only negating cards in battle.
