When using the Titan’s Challenge Instant, if there is an effect on the Boss Card, does the Titan gain the effect instead of the original Hero?
No, the Titan is simply taking all of the DMG for the Hero with his Instant, none of the effects.
When using the Titan’s Challenge Instant on a Hero in position 1 against Vrykolakas, does the Titan take the extra DMG from Weakness?
Yes, the Titan is taking all Boss DMG for the Hero he is protecting this turn and so the extra DMG is first applied to the protected Hero and then transferred to the Titan.