This won't address all the questions in your post, but the inventory screen doesn't need to be a separate scene. Depending on how you want it to work, it can instead be an overlay or otherwise part of the UI for the game, rendered using the built-in GUI system or implemented using other means.
As for making the data persistent, the most straightforward solution would probably be to store which/how many artifacts have been collected using PlayerPrefs (which will allow the data to persist between runs of the application as well as from scene to scene).