The "speeding in excess of 100mph" charge, CVC 22348(b), is a civil infraction. We do not issue arrest warrants for those. However, failure to appear (CVC 40508) is a crime, and this charge will become that soon.
On the speeding-over-100, you (or your lawyer) do need to face the judge; and that is so they can give you a stern warning, explain the future consequences for doing it again, and make you "scared straight". (straight is US slang for obeying the law).
Failure to appear = Emergency
Failure to appear, however, is a misdemeanor and will almost certainly result in a warrant for your arrest. This is an actual crime. It may be surprising that a civil infraction turns into a criminal matter if ignored, but that is exactly what happens. Given the language in the letter and the fact that you obviously missed your resolve-it date, that may have already happened.
Heading home without handling this properly is a novice mistake. Your only option now is to hire a lawyer, since you have left the country. Hire one who is local to the court your ticket is in - it should be a lawyer who knows the judges and staff, and isn't disliked by them. My favorite way to get lawyer referrals is call other nearby lawyers who do not practice in that area of law, and go "I'm sorry, do you know anyone who could help me?" Make 3-4 such calls, you'll start hearing the same name over and over.
FTA is a new, second charge, so that would be two charges. The upside is this makes it easier to plea-bargain since you now have two things to trade.
How to plead it
All this will happen at arraignment, which is only the initial phase; but given your options it will surely finish here. That is common in traffic matters.
If you had done this sooner, you could have pled not-guilty and asked for a proper trial (which is still a 2-3 minute affair). An order would be issued for the officer to come and testify. Generally if the officer appears, you lose, and if he doesn't, you're off scot-free. But you lost that opportunity.
Next you can say you do not wish to plead guilty to 111 mph but would plead guilty to 99 mph, and hope the judge will allow that. The reason to do this is to save a few hundred dollars (the point on your record and opportunity for traffic school doesn't matter to you). You are betting the judge doesn't want to waste time with a trial. (except now he knows there won't be a trial, oops). You can still try arguing it; good chance it will work.
However, if the failure to appear exists, it's more complicated. You must get that dismissed! You can argue your bona-fide effort to reach the courthouse previously. It would have helped if you were standing in front of him personally, obviously come quite a distance and effort to answer this charge, can't do that now, but judges are pretty sanguine about dismissing failure-to-appear if you really do appear (via lawyer is fine) willingly out of your own initiative Of course, this will only impress them if you do it right away.
The key is to resolve it together with the underlying ticket as a plea-bargain; if you already resolved the ticket, you have nothing to bargain with! So you ask the judge to dismiss the failure-to-appear if you plead guilty on the 99 mph. Or if that is not acceptable to the judge, ask to dismiss the FTA if you plead guilty on 111mph.
How do you argue this now you're gone?
I would have said to try trial-by-mail. However the CVC 22348(b) is crystal clear; you must show up in court in person: either you or your lawyer.
If the failure-to-appear was not a factor, I might have said try it anyway and see if it works. But it's a gamble; the judge may not have the freedom to waive the CVC 22348(b) requirement since you always can hire a lawyer.
However, dismissing the failure-to-appear is an absolute top priority. This would make you an international criminal, and that's not nearly as much fun as the James Bond movies make it out to be.
As such, I would say you are pretty much stuck with hiring a lawyer. Because he can manage every possible contingency. He's pretty much going to argue what I said above. You could've done it yourself if you'd done it sooner. Live and learn.
It really doesn't help your case that you were inside the USA the entire time the ticket was pending and you did nothing. They will feel like you consider their court a joke. On the other hand, if you retain a lawyer after you had already made your escape, that says you take your relationship with America seriously, and earlier was a novice mistake you own up to. They will not care that you fled the country since they would not have sent you to jail for this.
You need to do this right away. If you wait months -- or worse, if you put it off until the next time you want to visit the USA! -- it will be much, much worse. It happens all the time where a traveler clears the pre-check, arrives at JFK Airport, and gets denied entry because of something the pre-check missed and put on a plane back home (at his expense).
By the way, when you sign a traffic ticket in CA and many other states, you are not admitting guilt. You are swearing a promise to appear in court, which is part of a fair exchange: you promise to appear later, and they let you go now. If you are convicted of violating that promise, you won't be trusted in the future, and could be hauled to jail while you watch your friends be cited and released for the exact same charge.
And if an FTA remains unresolved, then the next time any state officer stops you for any reason, he will probably take you to jail. (he'll make a judgment call based on his ability and the seriousness of the underlying crime). Sorry, if you're sitting at JFK Airport, California will not pay to get you extradited (give you a free flight to CA) for a speeding ticket.
Also, if you had a CA driver's license, insted of 99 you'd plead 29 over the speed limit; 30-over disqualifies you for traffic school by mail, which would remove the point from your record.