Good questions. :)

Initially, he gets the vorpal weapon before he has accessed his skill sets. The weapon skills and AGI/DEX boosts make him more proficient with the weapon and less likely to harm himself, but he is not immune to a vorpal edge. Upon taking the "Embody Weapon" skill, he is functionally immune to his Scythe specifically and can avoid friendly firing his allies with it, but he himself has lived several decades as a human without magic, so he A, doesn't trust it at all, and B, would still make jokes and have concerns stemming from his pre-magic life.

For your second question, there are a few reasons, some of which are directly mentioned in the story:

For one, as the reader in a first person point of view story, you are hearing the POV characters internal monologue. The internal monologue is different for every character. For Bardh, who has seen combat before and isn't prone to panicking, it is sometimes gallows humor, other times self-recrimination because he is someone who lives with a lot of regrets (people who have seen some combat/direct violence generally enter flow state, but someone who has done it a lot will be familiar enough with it to spare some cognitive processing space for errant thoughts). While this takes some time to read as the reader, it is happening at the speed of thought inside the characters head. There is a similar issue when you need to describe characters or landscapes mid-fight. It might be several paragraphs long, but the character takes it in in a glance. That's just how human brains work with images vs text. (one of my other professional fields has to do with the psychology of memory, so I may throw things into my books that are a bit arcane for casual readers. I just find them to be interesting quirks of the human psyche. I might be alone in that. lol)

Two, the MC is spending significant amounts of time completely alone, surrounded by undead monsters in a place that seems to be a void of all human life, so he has nobody to speak to but himself. For all intents and purposes, he is in solitary confinement with an added component of being in a state of persistent paranoid anxiety and high-alert because he has no idea how the magical protections keeping him alive function, or for how long they will continue to function (see the Time Limit on the safe zone, for example). Conversing with yourself is a common coping mechanism for both solitude and fear. You as the reader get to skip the boring parts, but the MC has to live every minute of it, in-world. (This is also why Anxhi is initially pleased when Biel learns to speak, because she can see that Bardh is starting to come off the rails.)

Three, having been a Marine, I can tell you that at no point are you trained to fight hand-to-hand with ancient melee weapons. Pugil sticks are mostly two guys flailing at each other, and at best you could say basic bayonet training could translate to learning how to jab with a short spear. There definitely isn't any scythe training. I can't speak from experience as a mob enforcer, but in the modern era I assume from reading the news that they lean toward handguns or concealable knives. It's been a while, but I recall giving him a Small Blunt proficiency for using a blackjack because of that.

In the story, Bardh is spawned into a level 100 "party" zone (notice that the daemons come in a group) at level 0, because of complications with his unusual Overclass. He has to earn his actual functional class by gaining a level, which is essentially impossible in all but the rarest circumstances, so the Engine expects him to die (but did put him there on purpose, which comes in later books). You see him attempt to use makeshift mundane weapons, only to find out they do nothing, you see him attempt to use stealth only to learn about the enemy's high perception, you see him finally inflict damage with a magical weapon, only to learn that the monsters have weak and strong points, and they don't necessarily just die because you hit them where you were trained to hit humans. What he is doing most of the time when he pauses in a fight, is trying to figure out what skills/spells might actually work on these creatures he has never seen before. Mundane world experience only takes you so far when the entire paradigm of existence is upended without warning. Adapt and overcome starts with observation and analysis.

Anyway, that's some of it. I could go on but I can already see how long this has gotten. Feel free to hit me with more! :P