In SSB4, is it possible to counter the hit resulting from an opponent's counter? For instance, say that Samus and Ike are on the same team and the game settings prevent players on the same team from hurting each other. Say Ike is face-to-face with a Marth on the other team and Samus fires her power ball from behind Ike. If Marth counters the energy ball, his counter will hit Ike since they are standing close together. If Ike counters right before Marth's counter activates, would he counter Marth's counter hit and not take any damage, or do both counters hit?
You could technically counter a counter, but you would have to do this very quickly and it it extremely difficult. It is much easier when using an item that slows time. It also depends on if you have custom counters. If you counter a counter, then the first counter triggers your counter and only damages the one whose counter you countered.
Yes, but some counters make you invulnerable during their duration. In your scenario, Ike and Marth would hit each other, but neither would take damage.
A counter like the one Shulk has, would allow you to counter the opponent's counter and also hurt him, because Shulk pauses before he hits the opponent. This allows the opponent to get out of his invincibility first.
The counter window of most characters is pretty small. That is to say activating a counter by being hit by a counter is very difficult. It is in no way impossible, though.
However, many characters experience a period of invincibility before/during their counter. I know from experience it is not impossible to deal damage in a scenario similar to the one above, but the timing must be spot on. Because the invincibility only lasts a split second, you can still deal damage without taking it, but you almost are required to slow time to do so.