No, not the only one, but perhaps the country where it's done most blatantly.
Perhaps unique is the fact that the chief observer of elections in many states is elected to an office which has almost the sole purpose of running elections.
But as Antonio said, the departments that run election are usually in some way "partisan" in the sense that those running them aref from political parties
That's kind of a biased question. Few people have been caught committing voter fraud, that doesn't necessarily mean that there aren't a lot of cases that don't go unnoticed.
That said, it's not nearly enough of a problem that it has any effect on most elections.
Why do Republicans make it out to be a bigger problem than it is? It leads to lower turnout. Lower turnout is good for Republicans, generally speaking.
For the same reason that Republicans aren't. Expanding the electorate (legally or illegally) helps Democrats win elections.
That, of course, would only work for federal elections. Any further federal regulations would certainly be unconstitutional.
That's probably one of the main problems with nationwide popular vote efforts for President, that every state would still have their own standards.