The teleportation to Hydatos will be unlocked by reaching level 50.
When you enter Eureka, you can be in a party.
Talk to Rodney to enter Eureka And to re-enter Eureka next time, simply talk to him again.
However, I will ask what I feel is a really important question, which is What are we missing here? He will be able to upgrade your weapon to a regular version, and then to +1 and +2 versions, which are necessary for your Anemos weapon.
Which is just a fetch quest.
He will ask you to complete step 1: Broken Weapon.
This way, you will have sufficient time to gather up parties, and persuade them to go kill wraiths together.
If a Summoner Pet lands the killing blow on a mob, no experience will be awarded.