HAHA, that guys is nuts…
In terms of the energy weapons, we can make them recoil-less. I wonder if we need to explain in depth how it all works, or just accept that something powers the weapon, it fires a bolt and that bolt causes damage that we’ve described. We could have some bits that we know and can be detailed e.g. a weapon has a heat capacitor, there is a power cell etc.
Close Quarter weapons – look at Sulu’s weapon – he activates it into a longer sword. Could that be a solution rather than having it sheathed? You carry a smaller weapon that when activated gives a longer blade? With the size of the handheld weapon, you’d probably use that over anything that is a sword I would think. It is just to give people the chance to use it for coolness sake 😉
As for body armour, it could be a kind of jacket with a mesh inside to dissipate the energy. Maybe it also helps against attacks such as stabbing or slashing with a blade, almost like a modern day stab vest.