1) Many people believe there's a "correct" way to play Baroque music. And that one gets respect for playing Baroque music the correct way. Deviating from the correct way is seen as bad taste. Assuming that this viewpoint is right, how do we advance music? How do we create new styles?
Rather than a “correct way” there is a range of principles that should be followed when playing Baroque music. Many of these principles have been discovered fairly recently (mostly from the 1950s). Baroque music – contrary to Romantic music, for instance - is not a living tradition. It died a long time ago, so we con only make educated guesses as to what it should be like. It is a bit like being able to read and write a dead language, but having no idea how it was actually pronounced.
At the same time, even though there is a range of "correct" interpretations, there is also much that has just been shown to be incorrect. So it is not completely subjective and up to one´s taste.
Now, for the way to advance music, you already answered it in your next question: you create a new style! The way to advance music is not to play music of the past in a way that is fundamentally incorrect, but to compose new music. That has always been the case, even in Baroque times. J.S. Bach’s sons were not over impressed by their father’s style, so they invented the classical style. Beethoven was not happy with the classical style, so he invented romanticism. Even Liszt got tired of romantic music after a while and invented modern music.
2) Isn't it a purpose of music to please the ear? If so, what's wrong with Gould who brought new life to works such as the Goldberg?
This is perhaps the most important difference between Baroque music and the music which came afterwards. No, the purpose of music is not to please the ear or to entertain the audience – although in many cases it will display these side effects.
Music which has at its core the sole purpose of entertaining and pleasing the ear will have very little quality and last very little. We are talking pop music here. Of course there is nothing wrong with that. Except when you realise what is music´s true function and true potential. Then it becomes very wrong indeed. It is like finding a Ferrari stored in a barn into some farm. Then the farm tells you that a visitor left it there and never came back for it. Then he tells you that he is harnessing it to his horses and using it to carry manure. "What is wrong with that?" the farmer may ask to your great horror.

No, music is a language (or if prefer to be accurate, language is a music). As such its true purpose is to model the world in order to make it understandable to oneself and in order to communicate this model of the world to others. And this particular model goes beyond what ordinary language can model. So music is for speaking of things that cannot be spoken, to enlarge the limits of communication, to talk to oneself about that which cannot be talked about.
The Baroque musicians understood this very deeply, but such understanding has all but been lost. Music is no more a speech.

Or to put it in another way, imagine that you speak no Russian, but you overhear a conversation in Russian. You may find the sounds very beautiful and pleasing to the ear. And there is nothing wrong with that. But you will be missing the essence of Russian if you start believing that the whole purpose of that conversation is to please the ear. There is a meaning to the sounds, but it can only be conveyed to those who know the language.
3) If we insist on following the tradition, then why do we play Baroque music on instruments such as the modern piano? Bach could not have imagined that one day there would be such an instrument and therefore wrote music for it in advance!
Unfortunately, as I said, the tradition has been lost. At great pains researchers have been trying to recover it. Some of it has indeed been recovered, but much remains unknown, and sadly may never be known. There is no problem in playing Baroque music in whatever instrument, once you understand its essence, once you master its grammar, once you understand its speech. You will then be able to “speak” and convey its message. Unfortunately this is not what Gould (or Richter) did. I suggest you listen to Rosalyn Tureck, Angela Hewitt and Wolfgang Rubsam (you are in for a huge surprise with this one) to have a taste of what proper playing of Bach’s music is like.
Of course, I like Gould very much, just like I love Vitor Borge. But they are not playing it properly.
These threads also talk about this issue:
https://pianoforum.net/smf/index.php/topic,4736.msg44774.html#msg44774(how to play inventions – Escher picture – Example: Invention 4 – Analogy with the game of chess)
https://pianoforum.net/smf/index.php/topic,2632.msg22640.html#msg22640(pedalling in Bach preludes and fugues)
https://pianoforum.net/smf/index.php/topic,2585.msg23066.html#msg23066(unorthodox selection for competition – Rosen’s quote on Bach – Rosalyn Tureck wisdom and discussion of Baroque performance)
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https://pianoforum.net/smf/index.php/topic,3219.msg28310.html#msg28310(how to interpret Bach at the piano: as a harpsichord?)
https://pianoforum.net/smf/index.php/topic,4912.msg46590.html#msg46590(Books on the interpretation of Bach)
Best wishes,
Bernhard.