I have experience with:
Sword and Shield (used to be my favorite form, but I am getting old for it now)
1 handed sword (how you fight when you loose an arm)
Spears
Glaves (spear with a long knife on the end)
2 H-Sword
Rapier (thrusting)
Dagger
"Edge Control" is something that is VERY basic. The hilt is made such that it is difficult to swing and not have the edge in the right direction. I knew every time I struck flat, and called it accordingly, but this did not happen more than once every 3 months.
Positioning is more about range and angle of aspect to the target. Aslong as both are useful to the weapon, there is no real differnce between an axe and a sword for defencive purposes. A parry with a one handed weapon is done the same wiht all one handed weapons... Imagine holding a sword with your hand near your waist and the tip infront of your head. The block (parry) is done with the bottom half of the blade moving into the incoming swing, the tip does not move as moving it leaves it out of position to attack. The slick thing to do after the block is to swing your weapon following theirs as their attack leaves an opening usually. This is the basic A-Frame defence wihtout a sheild, and it works with all one handed weapons, and 2 handed come to think of it.
MMA is great... for unarmored combat. A wrestler, no matter how good, has to make sure to not get a hit and be able to grab his opponent. A person with a 36" blade has an effective range of 7ft. The big trick to beat lighter armored opponents is to not overcommit on the swing and leave yourself out of position. All one needs to do is connect if they are unarmored.
But if there are any significant differences between weapons such that you need to learn weapon skills differently, then there are different defenses against weapons.
Not enough to make it worthwhile to calculate. Defense is all about being able to block the incoming shot, not being where the shot is, or being in the right position so the shot does not have power. That last one is true skill, but power is generated by the swing and if one is too close before the weapon is swung, it doesn't matter the weapon.
His teacher says that all a gun is is a very long spear. That strikes me as completely absurd.
The teacher is not far off actually. Long thrusters are very similar to guns. I hold rapiers with my index finger going up the tang before the cup so I can point where I want the tip. My hand looks I am "shooting", thumb pointed up, index finger extended, and the rest curled to the palm (around the quillion). Even in a refused stance (where the swords hilts are behind the body and the points at the opponent), I am shooting them. Now think about a spear thrust when fully extended. The leading hand holds the spear so the spear is parallel to the forearm. One could extend his index finger and it would be very similar to a gun.
Shows like the deadlyist warrior are entertaining, but not accurate. In the Viking vs Samurai episode, the shield was classified as weapon. The viking word for shield was "spear catcher".