Yes, you can respond to a triggered ability because it uses the stack like any other spell or ability
And, if this card battles during the Battle Phase, you can inflict 2000 damage to your opponent Time Maiden By Tributing this card, you can add 1 Timelord monster with 0 ATK from your Deck to your hand
The reason Omens shuffle themselves into your library was to allow the designers to make the Dragons stronger, which is important in a set about Dragons
Its hard to be too critical of Yennett, Cryptic Sovereign
(Also, this matchup tends to tie a lot in a tournament environment, because both decks take a lot of time and reflexion to play and have the ability to come back from a Prize deficit, so early scooping is rare.) Perhaps a better way to deal with Giratina (and one that I expect in higher numbers in Liverpool) is Lost Box