artifacts disappearing

[remote pumice]

Read the item description carefully

This is not a bug, this is how they work

You have to install them or they disappear

And at the end of a mission they disappear regardless

They are only made to be temporary buffs during a mission

[split zenith]

To expand on what Orange has said, assuming that you're still doing the first few missions to get the Catamaran fully operational, you don't actually have the option to install them until you get the artifact cabinet, which sits by the ship core. In this instance, the only thing you can do with them is scrap them for materia before jumping (they don't tell you what they do, but I think they mention that they get rendered useless by jump space, or something?).

Either way, it's intended behavior that the artifacts are destroyed on jump, except when installed in the artifact cabinet

[gleaming cloak]

Then what artifacts do I give to the trader

[remote pumice]

When you get that quest you can install them and then you get credit

Artifact cabinet is across from iris

[night sphinx]

or across from the airlock, if its the smaller dart ship

[outer shadow]

There is also an artifact you can find that prevents them from disappearing, but you have to install it in the artifact cabinet first. Until you get that the description tells you to just feed them to the disassembler.