§1. Personal possessions, not properties, belong to the marched magus. The properties belong to the covenant. While the rooms (or small building, depending on covenant layout) making up a sanctum are under the sole control of a magus, they are a property of the covenant. It is very possible that there are things like enchanted items and books within a sanctum that are possessions of the covenant.
§2. So on pain of possible march, the covenant has to let anyone who wants in in and allow them to take whatever they want from the sanctum? If they take something they shouldn't have or damage covenant property, oh well the covenant has to wait till the next tribunal.
§3. It very much is. The only people that should be let in to gather arcane connections, leads, and possessions which will go to the successful marcher are the Quaesitoris. Otherwise you risk things like contamination and looting. The Quaesitor will want to secure the scenes. What you do not want is a random collection wandering about doing whatever they want.
[The Quaesitor can, and most likely will, allow so of the Marchers to go in with them. However those Marchers are observing. They should not be gathering things, casting spells, etc unless asked to by the Quaesitor. They for sure should not wander off to do their own thing.]
§4. I never said scrap the "spoils of war". However the spoils go to the victor rather than any randoms who show up first and "demand access". With anything left behind in the sanctum it needs to be determined what belongs to the marched and what belongs to the covenant. It needs to be held until the march is completed rather than risking bits and pieces disappearing into random marchers pockets.
§5. Agree. If any possessions remaining after the Victor(s) take their due would be doled out under inheritance law.
§6. Marchers have no claim to the possessions in the sanctum. Only the Victor(s) do and if done properly those items would have been documented and preserved by a Quaesitor.
There is a distinct difference between Marchers and the Victor(s). Anyone who chooses can be a Marcher, but just because they are does not grant them access or a claim to the Marched possessions. If such access if granted then many of those possessions might go missing and there is less to compensate the Victor.
Anyone "demanding access" can and should be blocked. Any doing this are likely to be the type in which random things "disappear into their pockets".
The Quaesitor is not going to demand, since they will not want to antagonize the remaining members of the Covenant. They have the authority to force it so will not be denied, which is why I said they will "ask" earlier. Doing it politely will get cooperation, questions honestly answered, and information not asked for offered up. They are also the ones with the specialized magic needed.
Open season bad. Controlled access good.