A counter is any mech that goes all out into defenses for 1 or 2 types of damage instead of being able to win against all 3. These types of mechs are characterized by instantly quitting if you happen to be using the one damage type they are not countering as they will always lose against it.
No
No
If you only use one type and are not running an energy free then yes
Not necessarily. You are trading your electric resistance for the ability to use your weapons even when drained. That being said, any mech whose majority of weapons use energy and lacks any energy modules is a counter.
Yes, that is their purpose
Well, not by the definition we use. Some mechs can have a split in wins if you execute the battle multiple times from different starting positions, accounting for RNG etc. A mech that can consistently defeat another mech is considered a counter to that mech.