1. Why can there be such huge differences that alter the characters and their interactions so drastically, even though the staging is supposedly the same?

Opera scores tend to have very little in the way of stage directions. The earlier the opera, the more likely that is to be true. This is also true of plays. For example, in Shakespeare's As You Like It, nearly every production has the players on stage gathered around Jaques in a circle when he explains that ducdame is "an invocation to draw fools into a circle," but this stage business is inferred from the spoken line, not made explicit by a stage direction.

As a consequence, one of the parameters of opera that has the most room for original creativity is the staging. Some directors use willfully anachronistic settings for one reason or another, a notable example being Peter Sellars' modern settings of Mozart operas (see https://en.wikipedia.org/wiki/Peter_Sellars). Even without such bold statements, the inference of various stage business from the material itself is a fine art. Some directors miss obvious opportunities -- perhaps knowingly. Other implied action may be debatable.

2. To what extent are singers free to shape their roles? Are they given only a framework of stage directions, with room left for personal interpretation or improvisation? (And doesn't this lead to chaos if every singer does that?)

This depends entirely on the director. Some productions are chaos; other directors will encourage personal contributions but have the skill to control any chaos that might arise; and yet others will give firmer constraints. (Compared with theatrical productions, opera will more likely lean toward firmer control by the director for a few reasons, notably the tendency of opera productions to be "double cast": to have most or even all major roles sung by multiple singers over the course of the run. Another reason will be the varying level of dramatic skill in the cast -- typically a secondary consideration in casting opera singers -- such that some singers may have difficulty adjusting to others' improvisation).

Considering the example of whether Cherubino and the Countess should kiss, you might ask yourself whether this would have happened in a court performance in Mozart's day. But regardless of whether the answer is yes or no, we can argue that a modern production, for a modern audience, is free to do the opposite. Modern audiences have modern sensibilities and varying awareness of the etiquette of the 18th century, and opera companies need to fill seats. An academic production is more likely have a goal of historical accuracy, but an opera company is likely to put that aside (to some degree or another) in the interest of attracting patrons.

3. How is an audience to evaluate a production when it can vary so much from one performance to another?

I don't quite understand why differences would be a problem. As with plays, various considerations can come into play, notably budget and other constraints on set construction. Yet we can evaluate different productions of different plays. An obvious point on which to evaluate the Mozart example is whether you agree with the decision for them to kiss -- or not to kiss -- and the manner of the kiss, etc. And, whether or not you agree with it, whether the director, the conductor, and the cast made the scene "work" dramatically. This is a matter of opinion. Different people will have different conclusions.

I hope you don't mean to ask how audiences can judge how "correct" a given production is. I judge opera productions on how successful they are. I love the idea of historically accurate productions of 18th century opera. But I don't know how 18th century operas were staged, do you? I don't particularly like the idea of Mozart in a New York City laundry room, yet Peter Sellars' productions are dramatically compelling and thought provoking (and, as a consequence, I've warmed to "unconventional" settings both in opera and in theater -- they're often self-conscious and artificial, but sometimes they work, and they can work very well).

If the music is performed well, the drama is cohesive, and the key dramatic moments succeed in moving me without seeming too artificial or contrived, I am satisfied. If two productions meet these goals but have significant differences in their staging, I will evaluate them as both excellent but different.

1. Why is there such difference?

I would say it would rather be weird if there was no difference. Like, ask 100 random people to draw a picture giving a vague description — it would be really strange not to get 100 quite different results.

Opera consists of more or less 5 parts: A libretto, music, choreography, stage design and costume design. The first two are considered to some extent as what makes the opera what it is, created by the librettist and the composer, and interpreted by singers, conductor and orchestra. But even there with some styles of opera there is a certain freedom of text and of music. In baroque music it is expected for singers to bring their own ornamentation, and in opera buffa it is not unprecedented for singers to add remarks not written such in the score or modifying the text a bit.

But the rest — choreography, stage design and costume design — are traditionally considered to fully a choice of interpretation, and are thus less components of the opera itself, but of the production. These are designed by different artists who often do explicitly not want to what everyone else is doing.

Successful opera production are even repeated, rented and sold (which makes sense, since these can cost a lot to design). This means that you may see the exact same production multiple times. But even then there is an individual aspect. Not opera production is exactly the same each evening, so once the cast is different, the artistic team is different even the same production may be quite different.

But usually you will see different productions. And thus the same opera can be very different when watching multiple times.

But even if you take the same production, same team, even same case — it is not unexpected for people changing up some things, and not quite getting it the same way. I’ve been in a quite successful production of Salome at the Salzburg Festival, which has thus been restaged the next year. Here the rehearsals started by people trying to remember how the details of the staging went. And some things were misremembered, some things were changed a little bit, so it was not exactly the same as the previous year.

2. What freedom do singers have?

That kind of depends on the director, the conductor, the choreographers. Sometimes these have very clear ideas how things should be, and some give more freedom. But mostly the main choices for what is seen on screen do not come from the singers.

Still, a director needs to take into account what the singers are comfortable doing. Not every actor might be comfortable with staging kisses, for instance.

3. How to evaluate?

Opera is not there to be evaluated, but to be heared, seen and enjoyed. You can still evaluate certain aspects like how well it is sung, how well it is played, if you like choreography, costumes, stage design, if you thing it supports the piece or if it is a bit arbitrary, if you can see artistic value in it ... But all of that is very subjective.

Still it is not the intention of opera to be easily rankable. It is not a standardized test system where each production can be graded exactly by how well they did.

When the D'Oyly Carte company held the rights to perform Gilbert & Sullivan's operas, they insisted on absolute fidelity to the original productions. Some considered this a virtue, others differed :-) But, as you say, some revivals are less strict.

I note that you find this unsettling. 'Why can't they get it right, then leave it alone?'. You certainly have a point!

We could extend the topic to Broadway musicals and subsequent movie versions. Often it's a good job. Occasionally there's a transformation - 'Cabaret' springs to mind. But sometimes there's an irritating dumbing-down.

May we all continue to notice, and to care!