That first pic, that is an over flow hose. It used to hang out of the bottom of the fairing about 3/4 of the way up the back end of the bike on the left side of the bike.
When I put my undertail on I shortened that hose about 6 inches and if runs out between the frame and plastic undertail section. I've never seen any fluid come out of it. I wanted to make sure it didn't drip on the chain.
The second hose no clue.
-Flash