I prosecute for a Local Authority so can help a bit....
1.you can write to the court and plead guilty, but if you can attend you should. Wear a suit, shine your shoes. Plead guilty. Apologise. And then lay on your reasons with a trowel. One of your kids was ill, your mum was dying, your wife's left you, whatever, but give some mitigation as to why you didn't stop/report it. (although if you've told plod something, stick to that make sure your story matches.) basically just be the most pathetic individual you can possibly be without being annoying. Works for my defendants every time. :-(
2. How long is a piece of string... Depends on the mood of the bench on the day and whatever mitigation you give.
3. Either in Court at the 1st hearing or by post, same thing. It's an automatically discount in the sentence, but generally you get more credit if you attend in person.
4. If you want, it will cost, you won't get legal aid so I sort of think why bother except a decent brief will defend you better than our ever will. They are great at making you look like a massive waste of skin. Which is what you want then to do.
Good luck.