Example 1: Yes
The effect of Cyber Dragon Infinity can negate the activation of any card effect, regardless of its location, as it does not specify any area in which the effect need be activated.
Once per turn, when a card or effect is activated (Quick Effect): You can detach 1 material from this card; negate the activation, and if you do, destroy it.
As for the destruction of the activated card: if the card or effect whose activation is negated is in a zone wherein it can be destroyed, it is destroyed. This includes the hand, field, main deck and extra deck. If a card or effect whose activation is negated exists in the GY or is banished, the activation will still be negated, but the card cannot be destroyed in those zones.
Example 2: Yes, the Negation Occurs; Results Depend
As with Cyber Dragon Infinity, since Crystal Wing Synchro Dragon does not specify any area in which the activated effect need exist, it can negate the activation of any monster effect regardless of location. Now, as to the question of what happens: this varies depending on what kind of effect you activate in your hand.
Certain monsters, such as D.D. Crow, activate their effects by discarding themselves from the hand. Supposing that a player activates D.D. Crow's effect, Crystal Wing can negate its activation. However, examine the remaining clause (in bold):
Once per turn, during either player's turn, when another monster's effect is activated: You can negate the activation, and if you do, destroy that monster, and if you do that, this card gains ATK equal to the destroyed monster's original ATK until the end of this turn.
So, the gaining of attack is wholly contingent upon the monster whose effect was negated also being destroyed as a result of Crystal Wing's effect.
As another example scenario, if a monster effect activates in the hand without discarding it, as is the case with the Danger! series of monsters, Crystal Wing can negate the activation and - provided the card is still in the hand when Crystal Wing's effect resolves - destroy that monster, and gain ATK equal to its original ATK.