If you don't want to check the map, the proof you need to convince Edmond he is dead can be found within the starting cell block. You could have completed it before jumping down the pit, but you can also do it later.
You will get back to that locked door again, with the required key.
With many skills you would concentrate on upgrading the existing skill in its box. For example, once you have learnt 2 handed slashing damage, if you wanted to increase your accuracy you would add the skill points to the existing box. If you wanted to also use a crushing weapon, you would have to learn that skill in a new skill box.
For the Identify Equipment skill, it would not make sense to learn it in more than one skill box, or have more than one character learn it. You could have both characters learn Repair, but it would probably be better to just have one character with the skill, and swap equipment when required from the other.
With magical attacks, there may be some cases where you would want to learn different versions of the same skill. For example, you might want a high damage, high mana fire spell for stronger monsters, and a lower damage fire spell to conserve mana with weaker creatures. Alternately, you may want one pure fire spell and one with fire and another damage type.
