How long before a decision is made on my relative's case?

It's really not possible to accurately respond to your questions without knowing more information about your family member's case such as the nature of the charges, the facts and circumstances involved and what stage of the criminal process the case is in at this time, etc. If your relative has a lawyer, I would ask that attorney as a starting point.

That would be 3 years.

On felonies the statute of limitations is a minimum of three years. If a misdemeanor they must file in one year.

I have to assume that charges have been filed and your relative is now in the criminal justice process. Different time limits apply to different procedural stages along the way from arraignment on the complaint to trial. Most defendants give what is called a general time waive. This means that the ordinary time limits do not apply and the next stage of the hearing can be set at any time no matter how long it takes. This usually happens when the case is serious, complicated, or the client is out of custody, giving the attorneys time to prepare the case and schedule the hearings and trial. If the client revokes his time waiver, the limits begin from that point in time. So, for instance, if he is past the preliminary hearing and waiting a trial date, generally, the prosecutor has 60 days (can be a little more complicated that this) within which to bring him to trial. If the client has never given a time waiver, from start to finish - that is, from initial arraignment on the complaint to trial, the limits add up to be roughly 3 months. I hope this helps. His attorney should be able to answer these questions for him.

Your relative has statutory rights to a speedy preliminary hearing and trial. They can only continue the case with his agreement and consent. This may be a tactical decision that he and his attorney have made - there's no way to guess as to what the evidence is or the reason for the delays. Only the attorney that actually represent your family member can answer.

Every person has speedy trial rights. If the case keeps getting pushed back, he/she must be waiving time. The DA cannot push anything back unless the defendant consents to waive time.

The defendant controls how long. He has a right to trial within 60 days of his arraignment in trial court unless he waives time. There can be a lot of sound reasons for the defendant to waive time. However, at any time the defendant can rescind his/her general time waiver and demand trial within 60 days. His/her attorney can best counsel them on the merits of doing so.