Can I have a shared connection with another player?

Yes, you can, but please follow the respective rules for shared internet connection. Which are the following:

§3) Sharing Means of Connection

Players, knowingly, sharing an Internet connection and/or a device and operating accounts on the same world may not interact with each other within the game (be it, but not limited to dueling).

It is not permitted for players sharing a means of connection to interact with the same third party (be it, but not limited to dueling) after at least 12 hours has passed between the actions.

It is allowed:

• to join the same Town and/or Alliance.
• to participate in the same Fort Battle or Adventure.
• to trade with each other.
• to use the bank transfer feature to transfer in-game cash to each other.

It is forbidden:

• to duel each other.
• to place bounties on each other.