In federal court, every final order of a district court is appealable to the Circuit Court of Appeals, as is every grant or denial of an injunction. Other preliminary rulings (including those granting or denying a TRO) are generally not appealable until the whole case is over. A further appeal from a federal court of appeals to SCOTUS is discretionary with SCOTUS.
On the state level, some states are somewhat different, but most follow the federal model.
What percentage of appeal cases are overturned?
The average is about 15-20%, IIRC.
Your generalization about appeals is correct. Because some Trump-related cases are pending in New York state courts, however, some FReepers may be interested in a respect in which New York state practice is unusual.
You note that, in the federal system and most states, appeals are largely restricted to final orders. In New York, by contrast, almost everything is appealable, including non-final (interlocutory) orders.
So far this has worked to Trump’s advantage. His interlocutory appeals have enabled him to delay the adverse consequences that would have otherwise ensued.