1st - Can you choose new targets for the effects of an Event copied by Visitor from the Spheres' Response?
To my knowledge, a former CCG era FAQ stated that you cannot, but this mostly kills Visitor's utility.
And, if copying the effect of an X cost card, what would be the X in the effect of the copy, the former Event's X or zero?
When you copy an event card's effect you are essentially reproducing the actual effect written on the card not the resultant effect of it being played. This means that Visitor from the Spheres will allow you to choose a new target, but it also means you must pay any additional cost associated with the effect, such as sacrificing a character or discarding a card from hand.
If X is determined by the cost to play that event, rather than in the effect itself (so X in the upper left hand corner or X being something like the number of insane characters in play) X will always equal 0 since you paid nothing for the card. If X is defined within the effect then it is that number at the time of copying the effect.
Te deja elegir nuevo objetivo (para que veais como le dan la vuelta a rulings anteriores si quieren) y X seria 0 en caso de la copia.