Can an attorney represent a client in another state than their own?

You need a lawyer in the state where the incident occurred.

Yes. The attorney has to be licensed by, or have Court permission, to practice in the forum State but the litigants can be anywhere.

Generally, an attorney can only represent a client a state in which they are licensed to practice law. An attorney who is not licensed to practice law in the state where the action must be filed may still be able to represent the client in that particular state action. The attorney must fulfill certain qualifications and have an attorney who is licensed in that state also represent the client in that state action. This is sometimes known as admission "pro hac vice".

No, the attorney would have to get a approval of that court. I think most states might say no. In Federal district court, which is the trial court, the judges routinely just swear you in. But if the accident occurred in one state and all the defendants live in that state, you probably have to sue in that state, especially if the deceased lived in that state, as there is no connection between the incident and the second state.