A few preliminary things. Make sure you get checked out if you were injured in the collision. Also make sure you've contacted your own insurance company to report the collision if you haven't yet. Most policies require you to do that to ensure coverage of the collision, under the "duty to cooperate" section.
OK - turning left at an intersection means you yield to all oncoming traffic. It is lawful to pass through an intersection with a traffic control device (stoplight) when it is green or yellow. When the light becomes red, your car must have entered the intersection for it to be considered illegal.
That being said, you were probably at fault. One factor which may contribute to the other driver's negligence is if you had established yourself in the intersection with enough time and space for him to safely stop his car in time to avoid a collision. That would require testimony of an eye-witness that could say without question he had enough time and opportunity to avoid hitting you. Again, this would not remove fault from you, but would split it between you and the other driver.
Getting your phone number wrong might be enough to get the ticket dismissed, but most judges would overlook such a small detail - especially since many people give officers the wrong number. Your name, the location of the infraction, the law cited on the ticket - get these wrong and it is likely the judge will dismiss the ticket.
The fact that the other driver didn't get cited for no insurance? It has nothing to do with whether you merited receiving a ticket or not, and won't be factored in at all.
One option you might consider is requesting a deferment. To defer the prosecution of an infraction means your asking the court for 12 months to prove you're a good driver. Get through the 12 months without another ticket, and this one falls away. Get another ticket during the 12 months? Then you pay for both plus court fees. I
f you suspect a ticket may be possible inside 12 months, ask for mitigation. Explain to the judge that you were doing what you thought was right and that you are generally a very cautious and careful driver. Most judges will reduce the amount of the citation by roughly 50%.
Also be aware that deferment can only be used once every seven years, and you still have to pay a court fee of $100. If the cost of the ticket is relatively small, get it mitigated, pay it, and be done with it.
Mr. Shaw gave such a thorough answer that I only have one thing to add: addressing your concern re: the other driver speeding. Case law indicates that if speeding only brought the other driver from point A to point B earlier and did nothing else to contribute to the accident, it's not a factor. I agree that it may most likely be considered by your insurer and the other driver's insurer in determing whether to apportion fault. But it does not exonerate you for liability.
It's not a great idea to represent yourself in traffic court. You do, however, have the constitutional right to do so. I would recommend spending an entire day in the traffic court to observe how judges handle self-represented defendants to get an idea of how irritated they get at amateur lawyering.
If you really want to represent yourself, you should purchase an hour of a traffic attorney's time to have her or him coach you on how to handle things.
A better choice is simply to hire an attorney.