Coolant tank and a mystery tube

After doing some research online and reviewing the repair manual for this car, my boyfriend determined that I need to replace the radiator cap and the coolant reservoir cap and hoses. There had been some issues with the coolant boiling in the reservoir. He disconnected the off the old reservoir cap/tubes, and I purchased new ones.
So, I have put in the new reservoir cap. One tube goes to the radiator, but is the other supposed to be left unattached to anything?

Also, I'm unsure if this is related, but there is a very thin tube that runs from the engine and splits in two directions. One is long and goes down somewhere I ant quite see, the other is short but I don't know where it goes. I have attached a picture of these tubes if that helps.

Thank you!