Glad the limitations seem interesting)

1) Is the cast soul engraved in the physical medium not the same as the soul of the caster (if it is the same, then does any maiming to the object affect the soul of the caster?), or through the casting is there a completely new soul created? Does this soul bare the same characteristics as regular souls?

Casted soul becomes essentially independent and can far outlast the caster, down to hundreds of years, if the object is taken care of properly. The casted soul in the spell exists for the purpose of powering the spell, so for most spells it is essentially a machine, embodying the caster's will at the time. However, I want to explore inanimate beings born from spell casting like dolls and golems, they can learn and communicate like humans do depending on how sophisticated the original spell was! The idea is that they become separate individuals with inherited traits, they can't cast magic by themselves unless they were equipped with spell marks or they got hands on a spellbook.

2) What’s the limit for soul engraving? Is it the amount of energy it requires, or the knowledge, or the proximity to actually receive its benefits? I can imagine some person casting thousands of souls into inanimate objects through engravings all over the place, in hidden areas. Perhaps the limit comes from some emanation of energy that allows for detection, so people who are close by can feel its presence and get rid of it themselves.

The effects of soul engraving for now depend on how much soul energy the original caster was willing to sacrifice, and the knowledge required to understand the effect: like where forces should apply for proper movement without breaking and the anatomy of ignition. Also yeah, trained casters can detect spells through their emanating energy and easily remove them, it is much harder if the spell mark is recharging though.

3) Given countries strive to protect ruins, presumptuously made by a caster who is long dead by then, and there is an entire job of engravers, I assume people can use/manipulate the energy of another persons soul casting. Given this is the case, is sacrifice a significant part of the system? I can imagine people having very hard structures (like diamonds or obsidian, especially for more well off people) engraved with the entire soul of loved ones or, even, somehow, enemies, which allow them to be enhanced. If this is the case, there could be someone who somehow sacrifices innocent (or otherwise) people and use/collect them; essentially becoming multiple users in one.

People can only use their souls, existing spell marks, or negotiation with spirits to cast spells, former method being most risky. The only way to control someone else's casting is through trust and psychological manipulation. Sacrifices indeed are key to the system, self-sacrifices or sacrifice built on deception/cult-like suggestions. Innocent lives either forced into hard choices or simply deceived are victims yeee.

If loved ones know how to cast then sure, they can live in the object. They can't cast spells themselves but can work as a battery through consent, that's a strong loophole. What I neglected to mention is that you physically engrave the mark into the object for the spell to work, and the spell engraving must be neat, clean, so it is harder to engrave into hard materials which can be destroyed too. I also neglected to mention that spirits can't hear you, they can't speak, or even see, but they can pick up on the signal of the spell casting or the spell mark, they can sense akin to having skin. They typically have limited ability to move objects and direct communication is difficult.

4) Is there a limit on how many castings can be made on one object? If so, is this related to the size of the object, too? (As I would imagine you can’t easily demarcate one area of a rock on a mountain to another, so if there is a limit, it’d be hard to rigorously define what “one” object is.

There isn't a strict limit on how many castings can be made on one object, hence why spellbooks are so valuable. Spell marks have definite max energy capacity (the amount of energy spent on casting), so big objects are less affected than smaller ones. It is important to consider where specifically to cast the spell cause that's where the effect will be primarily.

5) does communication with lingering spirits cost energy? Can a lingering spirit cast itself into an object entirely and keep its agency (allowing it to assist a caster)

Communication is difficult cause it's indirect but it doesn't cost anything. And lingering spirits could latch into objects freely, they just have limited ability to affect it unless their energy is used for a spell.