The fact that the Vampire Killer contains the soul of Leon's betrothed is never mentioned or referenced in the rest of the series, even in games developed after this game. The simple explanation may be that Leon never told anyone about the true origin of the whip, either due to shame over having to slay his girlfriend, or to avoid his family falling under the suspicion of practicing dark sorcery. The only other person alive who knew the secret was Rinaldo, who could easily be persuaded to keep silent out of loyalty to Leon.
As of Portrait of Ruin, they do confirm that the whip is sentient as it "remembers" the events of Symphony of the Night at least as you have to fight a copy of Richter Belmont to use it properly.
Sarah's soul being the source of Vampire Killer's power does help explain why some branches of the family may not be able to use the whip since one branch might be more "Leon" and have inherited more of the Belmont traits than another and Sarah's soul recognizes that in them.
By that same token, it also explains why the whip couldn't be used properly after Richter Belmont was brainwashed. The sense of betrayal that would have inspired, namely Sarah's power being used to help the forces of darkness, would be seen as an act of betrayal of the promise that Sarah sacrificed her soul for. It wasn't until WWII when Jonathan Morris purged the taint of Richter's betrayal that the whip could be used properly again.
Yet one factor of the whip, as shown in Castlevania: Portrait of Ruin is that even using it as a non-Belmont will steadily kill its user. This game reveals that it's due to a Blood Pact that was made in creating Vampire Killer, where in Rinaldo's words "[Leon's] blood accepts your hatred for the power to slay your kind". Because sub-families aren't part of Leon's blood, they haven't "accepted" her hatred and it lashes out at them in the form of draining their life. For a more Fridge Horror take, one could consider it a manifestation of Sara's vampirism given how it drains the life from humans like vampires do...
Mathias appearing at the end of the game with the Crimson Stone seems to come out of left field as you had only just heard about it not long ago. However, Mathias would know about it as he's been secretly an alchemist and Leon didn't know that, as stated in the opening cutscene. Since the Ebony and Crimson Stones were attempts at creating the Philosopher's Stone, the typical goal of all alchemists, it would make sense as to how Mathias knew of the stone and what it could do.
Death still attacks you after beating Walter in Joachim Mode. If Joachim killed Walter before Leon got there, Matthias didn't get to steal Walter's soul. Death attacks because he's pissed that Joachim ruined the plan.
There are two alternatives as well. The first alternative is that if this mode happens because Leon was killed by Joachim, it's likely that Death attacks not only because he ruined the plan, but Joachim also killed someone who was still a dear friend to Matthias.
The second alternative follows the same initial idea, that Leon was killed by Joachim. As we see in the cutscene after getting the Green Orb, Matthias has been watching Leon's journey through some form of astral projection. And given how Joachim's death seems to have him fade into purple particles fading into a certain direction in an airless room, it's likely that while Matthias was watching, he took the opportunity to poach Joachim's soul to become a vampire, and only took Walter's later. As we see in both this game and Portrait of Ruin, it takes time before one becomes a vampire. And Matthias was immediately sensed as one when he entered the scene. In short, Death was trying to give Matthias a helping of Joachim's soul because it'll take time for him to fully turn.
Initially, one has to wonder why many items are set amongst Bernhard Castle, and many more of them being secrets. One would figure that Walter would try to hide them, since they can be used against him, right? Well, considering the fact that Walter's entire motivation is It Amused Me and that the Ebony Stone makes him invincible, it's more plausible that Walter is giving his hunters weapons or things that would make them think they can claim victory, but that ultimately would never work on him. It's all ultimately to spice up the game!
It also helps that many of the items he places throughout can be powerful but useless for the area it's in. For example, how many times has a new player gotten the Fire, Thunder or Ice Whips and tried using them in their respective areas? The Anti-Souls Mystery Lab is full of fire enemies, making the Fire Whip mostly useless, the Ice Whip is barely effective on enemies in the Dark Palace of Waterfalls, and the plant beings and Gargoyles outright resist the Thunder Whip.
When it comes to this game, there is the initial complaint that upon beating it, you don't fight against Dracula, but Death instead. Why is this? Well, consider the factor that Matthias had just turned into a vampire. He has no idea of how to use his powers and would need to take the time to learn them. This is why Death serves as the final boss instead, as a newly turned Matthias would be disappointing.
Dracula has a knack for playing mind games and constantly sets up backup plans for his return. This makes a lot more sense, considering that he was Mathias, an infamous war strategist.
Lament of Innocence is a typical name for a Castlevania game and par for the course with the series, but it's also the name of the music for the upper floors of the "Pagoda of the Misty Moon" and typically associated as Leon's personal theme. That ends up making sense as Leon effectively loses his innocence by that point, having entered the castle an idealistic young ex-knight serving the church who has lost everything, his home, his title, and the woman he loved. The song is a mix of both upbeat badassery and almost sorrowful tunes, lamenting the loss of Leon's innocence and the vengeful man that will be born to father the Belmont Clan.
Effectively the game's title implies a Foregone Conclusion...Leon's innocence MUST be broken in order for the Belmont Clan to rise up. The game is about an idealist losing said idealism.
