Not a US lawyer, but I can take a crack at it.
Depends entirely on the merits of the appeal. If it’s an appeal because “I got convicted! that can’t be right!” probably not.
But if it’s an appeal based on a good argument that the trial judge erred in law in some way, with good research into the law to support the grounds of appeal, chances would be better.
As to actual stats about chances of success, I don’t know.
Yes. Normally an appeal goes to an appellate court where there is a panel of three or more judges who hear the appeal.
The purpose of the appeal is to review the lower court decision and to ensure that no error was made. It’s a general principle that when government authority is being exercised, there should always be a way to have the exercise of that authority reviewed. That’s particularly important in a criminal case, where the liberty of the individual is at stake.
However, there is one major difference between the trial judge and the appellate judges. The trial judge is the one who has had the benefit of hearing the witnesses directly and has assessed their credibility. The trial judge is thus in the best position to make findings of fact. On appeal, the trial judge’s findings of fact normally cannot be questioned, unless an error of law was involved (eg, the trial judge allowed a particular witness to testify on a matter that was not admissible under the rules of evidence, which is a legal test).
The function of the appellate judges is to review any alleged errors of law made by the trial judge in the course of the trial. They have the luxury of time: the trial judge knows the law, of course, but may have had to make a decision on a point of law on the spur of the moment in the trial (e.g. should a document be admitted?) without much time to consider it. The appellate judges can review the alleged errors of law with more time to consider it.
All of them, depending on the grounds of appeal. One argument is that the conviction was unsafe based on the overall evidence; that the court below made an unreasonable decision about the guilt of the accused. It could also be based on the rules of evidence (which is a subset of proper application of the law) or on other legal issues, such as whether there was a constitutional violation in some way (e.g the police got a confession from the accused while he was in custody, without giving a Miranda warning).
First, the onus is always on the appellant to convince the appellate court that an error was made, sufficient to set aside the conviction. That’s a high standard to meet. Second, the grounds of appeal normally have to been raised at the trial as well, so that the trial judge had an opportunity to consider the point. It’s not a complete do-over.