How do i expand my stables without premium moneys?

When do expedition results show up?

when are quests done and my pets available again?

Upgrade your Stable by finding blueprints and collecting the necessary materials to have your pet build the structure. They will get XP while doing it.

Expedition results? Like when you are exploring? There should be a bar on the side that updates. If you mean capturing pets there should be a menu at the bottom.

Also many things show up in your Reports area: http://beastkeeper.com/log