On the topic of ruins and loot, what was/is the standard policy regarding artifacts looted/acquired (either while adventuring or wartime), and what are some of the more noteworthy artifacts you and the other Companions have come across (aside from the Amulet of Kings, of course)? (And on that note, may I be so bold as to inquire what sort of family artifacts the Tharn family has/had?)
It's seen as a common courtesy to leave behind some dort of information about the relic you've taken: What it was, how you found it, vague outline of your plans with it, where to find you in case the person who came here next needs to contact you about it. Write in standard Cyrodillic, or if you have a brush and the time and will, in Daedric alphabet if you feel it is appropriate.
If the artifact is obviously cursed, it's nice to leave behind some blood splatters as a warning. It does not have to be your blood. If you are raiding into a Dwemer ruin, flip the switches and turn the valves back the way they were on your way out. You don't want that hot steam that was spewing into the corridor to build up somewhere deeper beneath in a boiler and blow the place up.
When it comes to handling the looted found relics, it's mostly case-by-case custom approach. I like to wash what I've found first, cold water, a bit of distilled alcohol to disinfect it. Not advisable for some crystals and most fine Dwemer machinery, though. Cleaning is a good step, though, it let's you see the details beneath the grime, and significantly lowers your chance of contracting some nasty disease when you cut yourself on it.
(Not so fun story, shortly I was estabilished as the Imperial Battlemage, the Guardians of the Vault brought to me a cursed crescent, the foul hex on it had already killed three of them in a a rather ugly and painful manner. After we cleansed it of rust, I gave the remaining five a very long talk about tetanus prevention and since then the only other curse that befell the Battlespire was from a werebat. The curse was rabies.)
As a rule of thumb, do not eat your artifact. Don't put it in your mouth either. If it is a drinking vessel, don't drink from it. If it is a cooking utensil or a piece fo silverware, contact a Daedric expert (an actual expert, not just self-proclaimed); almost all of us know the Haskill This Is An Emergecy message spell.
As for the artifacts and relics out family has obtained over the course of the years vast majority of them has been... Well, I suppose the polite term would be "repossessed". Not that long after the Soulburst I was netly shooed off the main stage and my less sensible relatives and progeny managed to missplace a lot of the family's posession.
Still, what remains and is of note
A set of daedric crescents. Honestly, I am still dumbstruck as to why Mannimarco let me keep them on my person during my stay in the Castle of the Worm. The staff is unparalleled. I've managed to fit it with a new handle, since the last one just shattered in my face a couple of years ago, and by the Eight, how did I manage to go without it for so long?
The Spoon of Repulsion. From Sheogorath's domain, I don't know if he already had it or if I am that special, but it was entrusted to my care to propel bad anons out of this blog's very inbox at high velocity. Not much goot as an actuall spoon, since it throws your meal across the room and through the wall.
A couple of Azura's crystals. Some of them are full, and I forgot with hwom and I am not eager to find out.
A blood-drinking longsword that melts with the wielder's flash if used for long enough. Probably the artifact that's been in our posession for the longest... and one that's seen the least use.
Mallion-Canae, a ring made of petrified flame. Not sure what it's good for besides as a pocket warmer.
Three sets of armor made of dragon bone. I am not sure if it counts as an artifact, since they are extremely new. Apparently the Rimmen Armory is running out of space, and since I caused it in the first place...
Two Tablets of Silk, the devices that allow access to the internet.
The Fang of Barbas, which to my knowledge does not actually come from Barbas, and while held it does not allow you to speak a lie. Less helpful than it sounds. Banned from the courts of Cyrodill.
A vial of what's supposed to be Namira's blood, although it has the physical properties of oil rather than blood. A viscous substance with no known antivenom. So toxic that looking at it with unshielded eyes kills.