the text on the card says you may "cast" it. so the answer is yes, it will work with kiln fiend and pyromancer's ascension.
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i take it back. just tested the deck, i see what you are trying to do with it. very nice.
lilliana's caress doesn't do anything in this deck other than deal damage when the opponent's hand is too large for them to handle. this may be a good card in the beginning of the game if you manage to get it and your draw cards on the field, but late in the game it can be useless once the opponent has enough mana to cast all the cards you gave him. consider playing mind rot, duress, mind shatter, psychic miasma
this could possibly win in 4 turns. turn 1> goblin soothsayer turn 2> goblin bushwhacker swing for 4 turn 3> goblin warchief swing for 6 turn 4> goblin king (mountainwalk) cast goblin war strike for 4 damage swing for 12
deathrender would be a nice card for this deck. a bit expensive for 4 though. nice deck.
i would get rid of fire servant simply because of the high mana cost. burn decks shouldnt really last long enough for you to get 6 or 7 mana on the field imo. maybe reverberate instead to give kiln fiend that much more power, or maybe plated geopede. also, arc runner is great when you've cleared the field with flame slash and/or searing blaze (arc trail is also very nice).