Does an FTA related to a speeding ticket ever expire in California?

You have a warrant. Warrants are forever. No, you can never get a license in any state until you deal with the ticket and comply with all requirements of the court, and DMV. To handle a warrant, you must turn yourself in to the issuing court, with or without an attorney. On misdemeanors and infractions like this, an attorney can appear in court without the defendant being present which is safer and avoids immediately being taken into custody. You'll try to negotiate a recall of the warrant[s] and bail reduction or OR release. You'll try to negotiate a plea bargain on any Failure to Appear charge that caused the warrant. You'll try to negotiate a plea bargain or take to trial the outstanding charge that caused the warrant. Turning yourself in voluntarily will result in a better outcome than being brought in chains to court after arrest on the warrant. That can happen if you come in contact with law enforcement or customs anywhere in the country. Effective plea-bargaining, using whatever legal defenses, facts and sympathies there may be, could possibly keep you out of jail, or at least dramatically reduce it. Your attorney might be able to negotiate a payment plan for the fine determined by the judge or DA in plea bargaining. Unless you're competent to effectively represent yourself in court against a professional prosecutor trying to put you in jail, most people hire an attorney who can. If serious about hiring counsel to help in this, feel free to contact me. If you can't afford the fine, or counsel, you can go to the public defenders office in that court and request they help you get them appointed.

The fines may be the least of your worries. If you have a failure to appear, there may be bench warrant out for your arrest. I suggest that you contact an experienced immigration/criminal defense attorney for a face-to-face consultation and give him/her all of the facts surrounding your situation. He/she would then be in a better position to analyze your case and advise you of your options.

Unlikely to expire.