What are the times and medals for each Imperial Level

These items are used to complete Imperial Assignments.

You can tap on the floor below your Arrivals floor (It is not named in the game, but some tips early-on explain its use) to see - and complete - the current assignment. These assignments require an increasing amount and variety of Imperial Items.

In short, stock piling helps with the imperial quests going forward. When you complete a quest, the next one may ask for an item that you have already stocked. So, in general, you will likely get paid back for those items you paid credits to generate. That said, you will do better in the long run building floors that generate credits as a means to make credits. And, if you are diverting too many credits to your inventory you will make less money over time.

In answer to the other portion of your question, many of the lesser items will re-appear in later quests, just in large quantities.